Bob's Logistics mod includes a few new tiers of belts, which can be a little annoying trying to use this (Or the circuit one) and Bob's, since the belts in the furnace/factory are slower than Bob's.

I don't use Bobs Logistics, exactly because of the incompatible belts. Incompatible for all my blueprints not only for this mod.
It was not a good idea (in terms of compatibility) to shift all tiers of belts, so I configured Bobs Logistics to use the default belts, so all works well.
Maybe after updating all mods to 1.1 i will have a look to this. but I cannot promise anything.

Hm. That's understandable.

What about changing the mod so that there's a second tier available, that operates a little slower, but doesn't have built-in loaders? I like both mods (The circuit factory and the big furnace) because they work WAY better than the basic factories, but setting them up to avoid the slow belts can be annoying.

I do not use both mods (not yet) ;-) I support DellAquila only.
I already had the idea of simply leaving the loaders out. Maybe I make an additional mod without loaders.
I will have a look, what I can do after upgrades are finished.

Tested with a new map (on Factorio 1.1.4)
There is no issue with the belts.
With and without bobs the furnace produces ca 22k iron plates/min with 6 speed modules
https://prnt.sc/vv8pi0, https://prnt.sc/vv8rkq
with 8 express belts (45/s) you can transport 21.600 items/s. this the maximum

Maybe I misunderstood you, and the only thing you want is a faster furnace with faster loaders?
Then this has nothing to do with bobs logistics and lead me on the wrong track.
There are more mods adding faster belts. I will have look, to support faster belts more generic.
Or do you want same speed furnace and use only fewer but faster belts?

Ok, now you can tweak the furnace with values you want.
Sample: double the output: https://prnt.sc/vvaynt
Maybe more options (less cheaty) if I have more time.