Here is a list of mods, I have found, that are aimed to restore CBT/TT rules (a note of caution, I have checked them with beta 1.2.3, haven't tested them with 1.3.1 yet, as many mods are now in process of adjusting to new patch):

Essential mods (required by others mods):
BattleTechModLoader (github originally by Mpstark, continued by janxious)
ModTek (github originally by Mpstark, continued by janxious)
CustomComponents (github by BattletechModders)
DynModLib (bithub by CptMoore)

Performance mods:
BattleTech_Turbine - decrease loading times (github by Sheep-y, also contributed by m22spencer)
BattleTechPerformanceFix - greatly improve UI performance (github by m22spencer)

Rules mods:
CBTHeat - removes damage from overheating, introduces rolls against ammo explosion and shutdown, penalty for accuracy and movement, not exactly TT rules but much better than van. (by McFistyBuns)
CBTMovement - restores ability to attack after sprinting, moving, sprinting and jumping now implies correct penalties, evasion pips are now permament - can only be removed by sensor lock (by McFistyBuns)
CBTPiloting - restores stability check after becoming unstable (by McFistyBuns)
Pansar - restores armour rules - total armour on section = 2xinternals (github by hokvel)
HardpointFixMod - biggest weapons are always visible, and restricts large LRMs according to TT rules (github by CptMoore)

CBT Balance Overhaul - restores proper damage values and heat generation for weapons, and many more (nexusmods by Aldodrem)
True Tabletop Conversion (TTC) - similar to CBT Balance, does not restore all values for weapons, introduces different chances like gunnery skill close to TT (nexusmods by BlueStryker)

(extensive mods)
MechEngineer - restores replacable fusion curos, engines, armor and structure components, actuators, gyros, cockpits and more (github by BattletechModders)
BT-WeaponRealizer - restores multishot, cluster fire (LB-X), introduce damage variance (github by janxious)

Interesting mods:
Arm weaponry can survive - not a rule, but nice (nexusmods by Lad09)
PanicSystem - chance of punching out (github by by BattletechModders)

Links for github: github.com/(user), for nexus: nexusmods.com/battletech and a search.

Note:
If more than one mod modifies one variable, they will overwrite themselfs. You will have to edit one mod and delete that variable. As usual Notepad++ is most desirable :) And WinMerge is the best tool to identify those variables as it can compare up to 3 folder structures and it's free :)