Stripping the jacket off the cables is not an option. The wires inside are only rated as part of a cable assembly, and cannot be used as individual wires.
I didn't check your numbers, but the process you followed is correct.
If you're dead set on installing cables, you might want to bump the conduit up a size. The extra space will make the pull a bit easier. Also make sure you use plenty of lube. Though since you're installing conduit anyway, consider installing individual wires instead of cables.
It also might make more sense to bump up the size of the feeder a bit, and eliminate the two branch circuits. Increase the size of the secondary panel, and supply the 20 ampere branch circuits from there instead. This might save money on materials, make the pull easier, and reduce the size of the conduit (not sure about this, as I haven't run any numbers).
Liquidtight
If by "LT" you mean Liquidtight flexible conduit (metallic or nonmetallic), and you're looking for protection from physical damage. That's not an option, since it's not permitted to be used where subject to physical damage.
PVC
You'll have to use schedule 80 PVC, to provide protection from physical damage.
Calculate Fill
To calculate conduit fill for cables, you treat each cable as a single conductor and calculate the fill based on the major diameter of the cable (looked up from manufacturer documentation). For Southwire® Romex® SIMpull® 12/2 with ground cable, the major diameter is listed at 410 mils.
A = πr²
A = π * ((410/2)/1000)²
A = π * (0.205)²
A = π * 0.042025
A = 0.13202543126711106084639258818232 in.²
Since you're using the conduit as a sleeve, and not a complete conduit system, you should be able to fill the conduit to 100%. However, filling to 100% will make it impossible to pull the cables, so you'll want to stay well below that.
3/4" Schedule 80 PVC has a total area of 0.409 in.², of which two 12/2 with ground NM-B cables will fill 65% of. Depending on how long the sleeve is, this might make it quite difficult to pull the cables through.
Fill = Conductor Area / Total Area
Fill = (0.132025 * 2) / 0.409
Fill = 0.26405 / 0.409
Fill = 0.6456 = 65%
To put this in perspective. If this was two wires in a complete conduit system, you'd only be able to fill to 31% of the total area of the conduit (0.127 in.²).
Wet and Damp Locations
If this area can be considered damp or wet, you'll have to use cable rated for wet/damp locations. In this case, you'll want to use UF-B cable (463 mil major diameter). Two of these cables will fill 82% of the conduit, making it nearly impossible to pull by hand (depending on the length).
Fill = (((π * ((463 / 1000) / 2)²) * 2) / 0.409) * 100
Fill = 82.33%
Best Answer
therobyouknow... If you google search something like " conductor size allowed in what size conduit " Like I did just now...You will come up with several charts to look at.. like this one.. https://www.constructionmonkey.com/calculations/electrical/tables/wireconduit
I'm in the United States, (and a Trump supporter so you may or may not like my answer, Joking..).. but for example if your main conductor size is #2 gauge,(and the wire size and insulation type are printed on the wire itself to out dummies like me figure this out)...then reading across the chart you would need 1 1/4" conduit for all 4 wires to be run inside safely. This assumes you know what type (copper or aluminium) wire you have and what degrees' in Celsius the wire will be operating at. Also what type of conduit your using and what type of insulation is on the wires, (see boxes above with drop down menu choices).. in the UK you should be able to find on line similar helpful charts.. Good Luck.. (BTW.. it's NEVER a bad idea to go up one size in conduit sizing.. just to be extra safe and in case you need to run an extra conductor in the future).. .