Gear Rifles - design assistance requested

[Varyon]

Took a bit to get back into messing with this, with how much of a downer Real Life has been recently (if you don't live under a rock, you probably know what I'm referring to; if you're currently literally living under rock because some a**hole looked at your country and cried "IwantitIwantitIwantit," you definitely know what I'm referring to), but at least for now, back to messing around with it. Things are coming together, but I'm a bit stuck where I always was with the firearm design - MinST. This seems like it would be the greater of whatever ST is needed to hold the weapon in place (I'm currently thinking one-handed firearms can be up to BL/2, while two-handed ones can be up to BL), and whatever ST is needed to manage recoil. That latter is the sticking point. I've read that some old British guidelines suggested no more than 20 lb-force of recoil for a service rifle, and that most modern service rifles are around 15 lb-force of recoil, so I'm tentatively saying something like the above - BL/2 for one-handed firearms, BL for two-handed ones. The issue is... I don't know how to calculate this for my gear rifles. I can work out the recoil energy for them, provided I ignore the secondary recoil from accelerating the working fluid (I think this can be done safely in this case). After messing with the math a bit*, it looks like the recoil energy is equal to the muzzle energy multiplied by the mass of the bullet, divided by the mass of the rifle - Rk = Bk*Bm/Rm. But that gives me energy, and the values I have to work with to set "Is this wieldable?" are in terms of force. Now, given that kinetic energy is equal to force times distance, I can get force by dividing by distance... but what distance is at play here? The length of the barrel? How far the rifle moves back while dumping its energy into the shooter's hands/shoulder? I'm thinking it's the latter but... what would that actually be, assuming a competent shooter with minimal or no padding? How much would it change if the shooter is wearing a gambeson or similar padding?

*For those playing along at home (and because I'd like someone to check my math to make certain I didn't screw something up), the variables of note are Bm (mass of the bullet), Bv (velocity of the bullet), Bk (muzzle energy), Rm (mass of the rifle), Rv (velocity of the rifle), and Rk (recoil energy). We start with conservation of momentum, which gives us
Bm*Bv = Rm*Rv (there should be a negative sign here, given velocity is a vector, but I only care about absolute values, so we ignore that)
We need kinetic energy in the equation, so we use
Bk = 0.5*Bm*Bv^2
Rk = 0.5*Rm*Rv^2
I opted to solve this for Bm and Rm, so that I could avoid needing to bother with square roots
Bm = 2*Bk/(Bv^2)
Rm = 2*Rk/(Rv^2)
Substituting these into the momentum equation (Bm*Bv = Rm*Rv), we get
2*Bk*Bv/(Bv^2) = 2*Rk*Rv/(Rv^2)
Which simplifies down to
Bk/Bv = Rk/Rv
And solving for Rk gives us
Rk = Rv*Bk/Bv
Of course, we don't know what velocity our rifle is getting accelerated to, and frankly we don't care. Fortunately, we can solve our momentum equation for Rv, giving us
Rv = Bm*Bv/Rm
Substituting this in with our recoil energy equation, we get
Rk = (Bm*Bv/Rm)*Bk/Bv
Which simplifies down to
Rk = Bk*Bm/Rm