I'm sure that you know that the voltage drop limits are just suggestions in the NEC, not something that would create compliance issues, but nevertheless they give some helpful and somewhat common to use limits that could be applied in a majority of installations.
OK, with the legal propaganda aside, you are posed with the issue of being able to deliver the proper voltage per KVA to the machine.
If the load is simply a Resistive load [Incandescent lamps or Resistance type element heaters], then the voltage drop will not be too much more than a nuisance. The lower voltage will lower the overall KW that the loads can use. This means dim Incandescent lamps and heaters that are producing less heat than would otherwise.
On the other hand, if the loads are Inductive [Ballasts, Motors, etc.], this can be a real problem. These components will try as hard as they can to draw the amount of KVA as needed. So when the voltage drops down, the current rises up - making the drawn KVA at the load consistent.
Since the subpanel you are planning to branch from is already limited by the #10s, that would be one of the last choices to use.
Sparky suggested to branch from the MDP. This would be better, if possible to get a switch out of it, or if overall possible. Otherwise, the subfeed might need to be upgraded.
Figure out what the voltage will be at the load, running through all points existing. If it's not too bad, or can be low without causing harm, it might be OK. Otherwise, opt to correct.
I definitely design to limit total voltage drop. I use the NEC's suggested levels as maximums for guidelines, unless a manufacturer's specs are more stringent. In some cases, the use of "Boost" transformers is very helpful. If you are unfamiliar with them, they are typical isolated transformers connected as to be Autotransformers in a series additive connection. I am sure you know of them well, but I added the info for those that may have not heard of them, or have not installed one but just heard the name "Buck and Boost"