I think you chose to lower the wrong stat.
Initial
S - 1 (Melee+2)
P - 5 (Ener+10, Lock+10, Expl+10)
E - 6 (Surv+12, Unarm+12)
C - 5 (Bart+10, Spch+10)
I - 10 (Med+20, Repr+20, Sci+20)
A - 5 (Guns+10, Sneak+10)
L - 8 (ALL +4)
SPECIAL TOTAL: +208
Also, all skills initially start at 2, so don't forget the extra (13*2)=+26 points]
Reasoning
Strength only controls Melee whereas Charisma controls Speech and Barter, resulting in a difference of 22(i.e. 2+10+10) - 14(i.e. 10+2+2) = 8. Luck at 9 will give the max of +5 to all skills, but that can be taken care of with an Implant later on, leaving more room to play with other skills via SPECIAL or Intense Training.
Traits
Add the two traits (Although you need to constantly find and wear glasses to keep you perception at 6 instead of 4 before any Intense Training or Implant).
This will add +10 skill points [PER(6) = 2 Ener + 2 Lock + 2 Expl) + (AGL(4) = 2 Guns + 2 Sneak)
Tags
Tag three skills (does not matter which I don't think) for another +45
Skill Books
Assuming 4 skill books per skill (4*3*13= +156)
Perks
Taking Educated at level 4 will net you a total of +32 skill points until level 20.
Taking Comprehension before you read ANY skill books will net you an extra +52 (1*13*4) skill points (assuming 4 skill books per skill).
Taking Tag! will net you another +15
Intense Training
This is the only other perk that will grant you more skill points; via SPECIAL.
I recommend 3 for P erception (with an Implant and Four Eyes will max to ten) since that controls three skills (3*2*3 = +18).
Mix 4 more among E ndurance, C harisma, or A gility; since P and I are maxed, S only controls 1 skill, and Luck will be maxed out skill wise via implant. (4*2*2= +16).
Remember: Distribute elsewhere if a skill is already at 9, implants will take each to 10 later on.
Note: This covers ALL of the perks you will get through level 20.
Implants
Only the implants that affect SPECIAL will raise skill points.
Remember: You will need 6 Endurance for 6 implants.
S (+2)
P (+6)
E (+4)
C (+4)
I (*MAXED*)
A (+4)
L (+13) [+1 to ALL 13 skills when luck goes from 8->9]
Total: +33
Level Ups
After already accounting for Educated and with INT at 10 you are left with 15 points per level for 19 more levels with (19 * 15) = +285.
Remember: Only distribute a maximum of 57 (including any additional tag value) to a single skill (Dead Money: 53), because of points gained via skill books (16[DM: 20]) and the on the corresponding maxed SPECIAL and 9 Luck (27) value.
Initial: 234
+ Traits: 10
+ Tags: 45
+ Books: 156
+ Perks: 99
+ Train: 34
+ Implnt: 33
+ Lvl: 285
____________
896
Which is 404 below the maximum of 1300 (100*13).
Dead Money
Adds 5 more levels and 13 more skill books.
5*17 = 85
4*13 = 52
And two more chances at Intense Training for E, C, or A = (2*2*2) = 8
Adding another +145 skill points.
Edit
I thought about it again and made some changes regarding luck, and some other things that were wrong.
Edit 2
This is going to end up being stupid long, but yes you can reach Max Skill Stats using clothing (which I kind of did already by relying on the 4 eyes perk) and skill magazines (utilizing the already added Comprehension perk) and you have the Dead Money DLC.
From the top:
You these two Traits:
- Small Frame
- Four Eyes
You need these three pieces of Clothing:
- The Followers Lab Coat
- Lucky Shades
- Motorunners Helmet
You need these Perks:
- Educated (must be taken at level 4, when you first can access it)
- Comprehension (must be taken before ANY skill books are read)
- Tag! (can be distributed to whatever you need at the time)
- Intense Training * 10
- You can get it 2 additional times during DM
- Use only on P, E, C, and A
- Only use it on P once
This leaves 4 available perks.
Total = Floor(35/2) = 17
17 - 1 - 1 - 1 - 10 = 4
This also assumes ALL of the skill books from New Vegas AND Dead Money. There are conflicting reports of one more Big Book of Science and one less Wasteland Survival guide. I will take that into consideration, but in the end it doesn't matter too much.
Initial -> Trait -> Clothing -> Implant -> Training
S - 1 -> Implant +1 : 2
P - 5 -> 4-E -1 -> LukyShds +3 -> MotosHelm +1 -> Implant +1 -> Train +1 : 10
E - 7 -> Implant +1 -> Train +2 : 10
C - 5 -> Implant +1 -> Train +4 : 10
I - 10 : 10
A - 5 -> S-F +1 -> -> Implant +1 -> Train +3 : 10
L - 7 -> LukyShds +1 -> Implant +1 : 9
I'll show the progression from least distributable points (skill dependent items or SPECIAL) to most distributable points (Tags and Level Ups). Note that this is out of any kind of in game chronological order, and I'm leaving out most of the step by step how to do it in a game (I'm not really up to writing a walk-through just yet).
This will establish a base on how to distribute the tags and leveling up points in game.
Initial -> Trait -> Implant -> Lucky Shades -> Moto's Helm -> Lab Coat -> Training : Skill Book
I'm doing it in this order so that I can do the Luck +1 ALL when adding on the Lucky Shades. Luck going from 7->8 doesn't effect any of the skills but I'm still counting that it happened during the add implants phase.
Skill = 2 + (Stat * 2) + Ceil(Luck/2)
My order of intense training is pretty arbitrary, but I need something solid here to base everything else off of. So I'm just doing top-down P, E, C, A. Everything will end up at 80 in the end (with some left over). But there is definitely room for variation in getting there within those 4 categories.
C - Barter - 16 -> 18 -> 19 -> 27 : 47
P - Energy - 16 -> 14 -> 16 -> 23 -> 25 -> 27 : 47
P - Explos - 16 -> 14 -> 16 -> 23 -> 25 -> 27 : 47
A - Guns - 16 -> 18 -> 20 -> 21 -> 25 : 45
P - LockPk - 16 -> 14 -> 16 -> 23 -> 25 -> 27 : 47
I - Med - 26 -> 27 -> 37 : 57
S - Melee - 10 -> 12 -> 13 -> 18 : 38
I - Repair - 26 -> 27 : 47
I - Scienc - 26 -> 27 -> 37 : 61
A - Sneak - 16 -> 18 -> 20 -> 21 -> 25 : 45
C - Speech - 16 -> 18 -> 19 -> 27 : 47
E - Surviv - 20 -> 22 -> 23 -> 27 : 43
E - Unarm - 20 -> 22 -> 23 -> 27 : 47
---------------------------------------------------------
618
To get all of the skills up to 80 (the effective maximum with skill magazines) you need (80*13)=1040 points.
The current base after all of the non-distributable points have been established is shown to be 618.
1040 - 618 = 422
Subtract the following:
Points you get from level ups through 25 (includes DM and Educated Perk): -402
Points you get from 4 tags (includes the Tag! Perk): -60
And you end up with 42 points to distribute as you see fit after each skill is at 80.
C - Barter - 47 -> Need 33
P - Energy - 47 -> Need 33
P - Explos - 47 -> Need 33
A - Guns - 45 -> Tag 60 -> Need 20
P - LockPk - 47 -> Need 33
I - Med - 57 -> Need 23
S - Melee - 38 -> Tag 53 -> Need 27
I - Repair - 47 -> Need 33
I - Scienc - 61 -> Need 19
A - Sneak - 45 -> Tag 60 -> Need 20
C - Speech - 47 -> Need 33
E - Surviv - 43 -> Tag 58 -> Need 22
E - Unarm - 47 -> Need 33
-------------------------------------
Need 362 from leveling
Again this is an effective maximum at 80, because you can get to 100 if you need to via a skill magazine. This is all theoretical, and probably a hard build, because you need to get into Caesar's safe house to get the lucky shades AND for the most part you're walking around with a Strength of 1 or 2. There is some fine tuning that could be made, but that is neither here nor there, in the end it is possible using this definition of a "Max Stats".
Best Answer
Unlike Gold in Skyrim, Caps are not considered a manipulable inventory item in the F:NV Engine. Your caps are kept in a separate counter at the top of the inventory window.