I've been doing some thinking about this recently. I'm not aware of any published contract system that does exactly what you want - so I'm writing one. There are two obvious measures of a unit's asset value: the BV (as a metagame measure of combat power) and the cash (C-Bill) value of the mech assets. (Cash values are listed on all the recent edition record sheets, and many of the old ones.) It will also help improve the plausibility of the contracts if the bargaining point costs for each section reflect the specific nature of the contract a little more.
Now the question is where to add these assets into the contract negotiations.
There are two obvious places where the assumptions of FM: Mercs lead to the problem you describe, and both are easily changed. The first is, as you correctly point out, the base monthly pay need not (and should not) be derived from salary alone. Adding about 0.1 to 0.3% of the base cash value of the mech/vehicle assets deployed to the base salary makes a large, but plausible, difference to the result. This not only represents the actual battlefield effectiveness of the unit better in negotiation, it brings a fraction of the asset cost under the payment multipliers - which increase for riskier missions.
This percentage should itself be something to bargain over - I haven't tested calculations properly yet, but try a base of 0.1% for 5 bargaining points, to a maximum of 0.3 to 0.5%. Add 5 points to the base bargaining pool, so that the first 0.1% is effectively free (unless voluntarily relinquished for points elsewhere). (Infantry-only units don't get this 5 point freebie. They just don't have the prestige. Poor ground-pounders.)
The other crucial area to change is not the salvage rights, but the support rights section of the contract. Firstly, note that battle loss compensation covers "equipment destroyed or damaged in combat", which should certainly include mechs and vehicles. FM: Mercs assumes an employer typically offers only (some fraction of maintenance costs) or (some small proportion of battlefield repairs). This is unlikely as written, as it simply fails to compensate mercs for their ongoing costs and capital asset risk.
(An example quick, crude fix would be to ignore all other changes and have the base Battle Loss Compensation, before offers, be 100% instead of 0%, reversing the order so employer bids it down first. However, this is a poor fix. It's unlikely in-universe, as it means large units make no profit over small ones on garrison duty, and employers would never sign such a contract, as it gives mercs no reason to minimise costs to the employer.)
I recommend that garrison, cadre, riot duty and most 'quiet' security contracts default to providing both types of support right, instead of the employer knocking off 20 bargaining points by doing so. This should save enough points for the mercs to go for a high percentage of everyday maintenance costs, or of combat losses.
(Yes, this seems backward compared to combat contracts, but it's not. In garrison-type contracts, the employer doesn't expect to actually need to pay anything for battlefield losses, and the merc unit doesn't expect much salvage. That's why mercs take those contracts, for low profit, low risk recovery-and-training time.)
Other changes should also reflect the nature of the contracts more.
'Combat' contracts, especially high-risk 'Extraction', 'Objective Raid' and 'Assault' contracts, should add a higher percentage of the unit asset value to the base salary. For high-risk short-term missions, have unit assets added to the base salary at a much cheaper rate - maybe as little as 2 bargaining points per 0.1% - and with a higher cap, say 2.5%. This reflects the employer assuming, and paying for, some combat losses. (Experiment, but don't go too high - remember these figures will be multiplied by about a factor of 6 or 7 once all the mission/employer/unit rating multipliers kick in.)
Salvage rights for many 'Diversion' and 'Extraction' missions should be worth less, probably 5 bargaining points less than usual for the employer (or reduce all the buy-back modifiers by x1), simply because those missions often won't give you time to salvage at all.
'Guerilla' contracts should definitely have battle-loss compensation bought at reduced cost in bargaining points for the mercs; try half-cost. These contracts expect massive risk to the mercs and a prolonged period out of supply surviving on salvage; mercs would expect some chance of making good their losses. Possibly, offering full salvage rights should only gain the employer 15, not 30, bargaining points on a guerilla contract.
I'd also suggest the addition of a 'risky garrison' clause. For some number of bargaining points (I suggest around 3-5), the contract states that 'garrison' pay assumes routine duty, and in the event of an actual planetary invasion pay increases to the 'defensive campaign' rate. (This should also kick-in the .5 extra "fighting the Clans" bonus, in the event of a Clan attack.)
I'm still looking at this issue, so comments welcome.
(Additional note on cash vs BV:
I prefer to work with cash value of 'mechs/vehicles as this fits better with the universe feel, but some games may prefer to use BV. Begin by fluff-texting the BV into the universe; given the organised nature of BTech mercs, I'd suggest making it an official MRBC-maintained statistical measure of a vehicle's historically proven battlefield effectiveness.
Now make the BV contributed by the unit an addition to the base mission pay. As a starting point, try adding 5x the total unit BV to the base crew salaries before calculating the monthly contract pay. Consider reducing the 'garrison duty', 'riot duty' and 'cadre' payment multipliers a little, as these missions won't typically involve major capital asset risks.
Alternatively, add this into the battlefield losses section, by figuring out a cash multiplier for the 'loss value' of a mech of given BV, and use this for the contract - I recommend about C3000 x BV to start with, but I haven't tried it myself, so test. Note that smart players will exploit this, as BV varies less than cash cost, so whatever figure you pick, light mechs will be 'worth' more than their face cash value, especially some very effective light-to-medium designs, and assault mechs 'worth' less.)