What kind of movement is this...manufacturer's  name.

There is no reason why you cannot replace the springs.

Repairers who were working many years ago will remember the Mauthe spring driven chime movements in floor clock cases. They were famous for broken mainsprings. I did a chapter on this movement for my book Chime Clock Repair. It has been a long time since I checked, but it may not be possible to find good matches for one or more of the original Mauthe mainsprings today.
Now, as for your question. Is it possible to convert a movement like this to weight drive? Yes, but it is not practical. A hobbyist might try it as a challenge, but it would be much better for you and for the customer if you obtain a new Hermle movement as a replacement. There may be some problems to solve in fitting a different brand of movement to the case, but these problems are small when compared to the effort needed to convert the old Mauthe movement to a weight drive. You would need to to obtain (or make!) three chain wheels of the right configuration and main wheel tooth size to fit the movement. You would also have to determine that the gearing would work out, so that an average chain wheel with, say, a 10-pound weight on it would power the gear train. You would of course have to look at all three gear trains.

I have never heard of a spring that could not be replaced. There are sources for custom mainsprings, if a close, standard spring cannot be shortened.

The cost of a custom spring would be a lot cheaper and original to the clock, than converting it to a weight driven.

And shortening a stock spring would be a lot less work.

The movement was not designed to be weight driven and who knows what unexpected problems you might bump into or if the change in the power source might increase internal wear.