I see you have three problems, which you reasonably note may be related:
- Too much heat on the oven side
- Too little heat on the proofing side
- Too little humidity on the proofing side, due to heating the air
While a heat pump will certainly solve your problem, I claim that it might actually be overkill. You see, a heat pump is necessary when you wish to pump heat from a cold source to a warm sink (which is the opposite of the direction it will flow naturally). On the other hand, you already have a hot oven room and a cold proofing room, and really, you just want the heat to go from hot to cold. So let it. Just let the air circulate between the two rooms, until they reach equilibrium. Of course, this may not be appropriate, so let's examine the assumptions.
I'm not a professional baker, but a quick search indicates that the proofing room should probably run about 30°C/90°F, 75% relative humidity (RH). Is that correct? You would probably like the oven room to run closer to 20°C/70°F, but the ovens are putting out a bunch of heat, especially when you open them up to put stuff in or take it out. Also, hot product coming out of the oven will warm up the room.
If the oven room gets close to the desired proofing temp, then you really do just want to blow that hot air over into the proofing room. But even if the oven room doesn't get that hot, simple convection might work. After all, the oven room is probably not a uniform temperature. The air right next to the ovens is much warmer than the air on the other side of the room. The important point is that you mainly want to draw the air immediately surrounding your ovens into the proofing room, and blow the colder air from the proofer back over your ovens. If the air next to the ovens is close to the desired proofer temp, or even above (which is best), then this could work.
However, if you just blow air around in a circle, the ovens will still be as hot as the proofer, which only solves one of your problems. So let's introduce another tool. Instead of just driving air between the rooms through ducts using a simple fan, let's use a fan to blow air from the oven to the proofer, but an evaporative cooler to blow it from the proofer to the oven. This will do a few things.
First, the "swamp cooler" will cool air coming from the proofing room, so your oven room is not too hot. Second, it will humidify the air to 80-90% RH. You don't really want your oven room to be humid, but you do want the proofer room to be above-average (which is why you employ the humidifier). So you don't want to just blow the cool, humid proofer air into your oven room. You want to blow it onto your ovens to cool the ovens and heat the air.
Ideally, the now-warmed, extra-humid air will get sucked in by the fan and blown into your proofer room.
It's possible, even likely, that this setup will not give you the exact temperature and humidity that you are targeting. But, it is likely to move the most heat for the lowest cost, while also giving you a humidity boost, all for the cost of some minimal ducting, a fan, and an evaporative cooler (much cheaper than any AC or heat pump both to acquire and to operate). You may still need to run a heater in the proofing room, but hopefully you will use much less energy to achieve the desired temp. The same goes for the humidifier. And ideally, the oven room will cool down to a more pleasant level.
It's hard to say how to size the necessary components, but hopefully HVAC folks can perform the necessary computations for you and give you a reasonable estimate without selling you their most expensive hardware.