Originally Posted by
Ron Damon
What would be helpful is a straight-on image of the rear wheel and the RD so we could actually gauge ground clearance.
Example of straight on image:
GS on 53-406
Your GS RD looks like an pre-2017 Deore with a max cog capacity of 36t. Nowadays and since 2017 Deore GS has been able to span at least 42t.
Riese & Müller mount a Shimano RD-T610-SGS derailleur on the Birdy which is OK because 36t is about the maximum possible on the Birdy 3.
The stopper for the rear arm folding is circled in red in the picture below which also show the position of a Shimano Ultegra RD-R8000-GS derailleur on the Birdy with 50x355 tires in its worst case position (the cage is the closest to the ground on the cogs in the middle of the cassette, its higher on the biggest and smallest cogs, on your picture, the derailleur cage isn't in its worst case = closest to the ground position).
About the gearing, if you are satisfied with 52x11 as longest which is about 6.7m, you could as well use a 9-34 cassette with a 42t chainring that also gives about 6.7m as longest and gives about 1.7m on the biggest 34t sprocket what is the same as what you will have with the inner small 39t chainring of your double and a 32t cog.