What’s the fastest way to make money in Sleeping Dogs

I assume GOTY includes all DLC listed in Steam under the DLC pack. The only way I know about to actually "deactivate" a DLC is asking Steam support to permanently remove it from your account without any refunds. So I can only give you a list of the benefits provided by the DLCs here and you have to be honest with yourself to not "use" them, e.g. always consider yourself to be 200k poorer than you are:

• I'll skip the cars, clothes and weapons, since they shouldn't be difficult to notice - basically you don't own anything but a motorbike and your own clothes in the beginning
• Police Protection Pack: Apart from the SWAT stuff it adds the "High Speed" mission and gives you some police XP (not enough for a full point on its own though)
• The High Roller Pack: $200k and premature access to the Tuono vehicle and High Roller outfit
• Martial Arts Pack gives you slight Triad XP boost (again not enough for a point on its own, but still...)
• The Red Envelope Pack: those red envelopes scattered around town containing $50k each
• Top Dog Gold Pack / Top Dog Silver Pack: A total of both 8 police and triad skill points
• The Zodiac Tournament: That tournament

So in summary, if you don't want to use the too severe DLC bonuses, don't collect the red envelopes and always leave $200k and 8 triad/police skill point unused...

If you're on PC (or can somehow access the respective files on your console), you can remove/rename the respective files (and probably have to deactivate updates for the game) I found a list of the DLCs' respective filenames here, extended by me on how cheat-y they are:

1E6323E1.dat Top Dog Gold Pack # pure cheat
576E446C.dat Top Dog Silver Pack # pure cheat
AC8D6F78.dat High Roller Pack # pure cheat
E58008F5.dat Red Envelope Pack # cheat, but you have to search them
E80C9CFE.dat police protection pack # swat clothes/vehicles, high speed mission (farm police XP)
3E97A062.dat Tactical Soldier Pack # clothes & weapons
8C79ECFB.dat Retro Triad Pack # clothes
67EE992C.dat Martial Arts Pack # clothes, dummy, shaolin showdown mission (farm triad XP)
81F578F0.dat Dragon Master Pack # collection of other DLC
613E5E9C.dat Square Enix Character Pack # clothes
849D8C70.dat Street Racer Pack # additional races
B41D5130.dat Community Gift Pack # ???
BA29F60B.dat Ghost Pig Pack # clothes
CD90EBFD.dat Screen Legends Pack # clothes, sword
D500D5B5.dat Deep Undercover Pack # clothes, car, CB radio
F3249186.dat Gangland Style Pack # tattoos
FD1036BD.dat Valve T-Shirt Pack # clothes
779AC7EF.dat SWAT Pack # cop mission (clothes?)
5AE2D067.dat Drunken Fist Pack # clothes
9ADD7588.dat Monkey King Pack # clothes, cloud-bike
41CADD1F.dat Law Enforcer Pack # HKPD clothes & cars
28333911.dat Movie Masters Pack # clothes
C8F81F7D.dat Triad Enforcer Pack # clothes, car
7A1653E4.dat gsp pack # clothes

Story DLC:
D3D01205.dat Wheels of Fury # mission for/with powerful car
E0E8FC75.dat Zodiac Tournament Pack
13EFB7EA.dat Nightmare in North Point # separate from main game
????????.dat Year of the Snake # separate from main game

You can continue to gain your Triad XP after completing the story by replaying the Triad missions. The amount of XP given for replaying a mission is equivalent to the difference between your final score and the highest score from your previous attempts at the same mission as long as it's greater than 0. There are clothing sets that you can wear that increase your Triad XP gain (5%, 10% and 15%). Here is a set that gives you 15%:

• J. Jiggler Straight Leg Jeans ($21,620 from Achete)
• Couronne Puffy Vest Red ($28,800 from Bruno James)
• Achete Stand Up Boots Black with Brown Sole ($17,400 from Bruno James)

Both shops are found in Central.

You should, theoretically, be able to get max Police XP before completing the story. In case you don't, you can gain them by replaying Police missions. You might have also noticed that there are optional drug bust missions (light blue police shield icon on the map) dotted all around the map, 17 in total IIRC. These missions will also give you a good chunk of Police XP. You should get the achievement associated with unlocking all 10 police upgrades way before the Triad one.

All missions can be replayed from START > Social Hub > Missions.