what is the right verb for the overall process of "conducting" a thesis?

You could describe the overall process of researching and writing a thesis as pursuing a thesis (as used here).

So you could write:

I would like to thank Zaphod Beeblebrox for the opportunity to pursue my thesis at Intergalactic Digital Research.

I know this is an ancient question but I will add a link from Harvard University website for future viewers.

I think it answers some basic questions. There are 'writing a thesis', 'purusing a thesis' (as the title refers to), 'conducting research' and even 'doing a thesis' in the article(s) the link leads to.

Here is the link:

Should you pursue the thesis?

In my experience, writing a thesis is generally understood, in context, to include the research work that the thesis is about. I think it would suffice to say:

I would like to thank Bill Lumbergh for the opportunity to write my thesis at Initech.

I would suggest 'working on' as the best answer