bisecting gnu make

[DSB]

Background situation: we're seeing an error that manifests reliably when
make 4.4.1 is used but not with 4.3. This isn't necessarily a make problem,
there are many other tools involved, but the insight we have is that 4.41
reliably triggers it vs 4.3. Therefore I'm trying to narrow it down by
doing a git bisect on the GNU make source repo.

Git bisect per se is straightforward but it turns out to be quite tricky in
the context of the GNU make build model. For instance, if a new .c file is
added a previously generated makefile won't work at that bisection point,
if a .h file was removed the generated .Po files will cause an abort, etc.
But starting from scratch each time with ./bootstrap runs into other issues
such as a change to the automake version requirement. Nothing I've tried
seems to work reliably across the bisection.

But I assume that all, or at least almost all, commits to git between 4.3
and 4.4.1 were buildable for GNU Make developers at the time.

So my question is: has anyone done this before? Is there a scripted way to
reliably build make at each bisection point (assuming 4.3 as the minimum)?

Thx,
David