Is thin winding at the bridge bad?

Well,
hello everyone. Long-time lurker here. Under normal circumstances I just read all your conversations here or use the search for problem solving, but today I came across a, for me, very new problem.

Today my first ever package of flatwounds (LaBella 760FS-B Deep Talkin')
were delivered and beforehand I precisely looked up the measurements of the flatwounds, and for safety I measured my bass (Yamaha TRB1005J) also, because I knew it would a be a close fit at the nut before the winding gets thinner.
BUT I knew not that at the other end, at the bridge, the winding would be also thinner for a long stretch. So here is the situation:

At the nut, it fits, BUT
at the bridge it does not fit?

Is this bad? Would there be any harm on the long run if the thinner stretch lies upon the bridge? For now, I put on the old roundwound B-string again while I'm waiting for your advice.

I hope this thread doesn't exist already, and if so: sorry! And thank you in advance!

 

Thank you very much.