I think coherentism is an important way at looking at how mathematics is actually done in practise, although I don't know of any philosopers that have looked at this in this way.
Truth is obviously important, but one has to add a qualifier that the truth is actually significant. There are lots of true theorems that mathematicians aren't interested in.
Take an example: Algebraic geometry.
a. Its generally taken that it was the Italian School in the 19C that originated this subject. They had a series of results that were 'intuitive' that is there were gaps in there reasoning or places where the reasoning was obscure. For example the idea og a 'generic element'. But the whole seemed to hang together - that is it formed a coherent system of results. And they were important as they pointed to a new way of looking at algebra & geometry together.
b. It was then Zariski that decided these results had to be put on a serious & formal basis. This impelled his work on commutative ring theory.
c. Grothendieck then applied the newly established Category Theory to place algebraic on what seemed the correct framework - the theory of schemes.
What this shows is that as a set of results which points towards a new theory and conjectures which one hopes & expects to be true to build this theory new horizons are breaking out, some of which transform how one looks at old results and some of which consolidates.
As one builds a theory one can build a series of conjectures that establish the framework within which one expects the theory to be built.
For example: representation theory of groups. This is a huge area with important links to physics. For finite groups the theory is easily worked out, for compact ones although using different methods they have exactly corresponding results. This bear out the mathematical intuition or rule-of-thumb that in the continuous case compactness is similar to finiteness in the discrete case. In the construction of the theory conjectures would be established bearing out this rule-of-thumb.
I think the whole issue of mathematical relativism is a deep and difficult issue. I prefer the idea of plurality & process. Mathematics is a tradition, and there are many different perspectives within this body of thinking which have their own standards of truth, justification & methods of proof.