Detailed Instructions: Given a travel related situation, and given a specific question about the situation, summarize the question into a title
Q: Here's my situation: I'm a UK citizen. I have an H-1B visa to work in the US as of 1 August. I also have a valid ESTA.

I would like to go to the US in July for a holiday, immediately prior to beginning my work. The holiday would be at the other end of the country from my work.

I can't enter with the H-1B as I can only enter the US on that visa 10 days prior to starting work.

Specific question: Would it be possible to visit the US in early July on the VWP, visit Canada/Mexico for a few days in late July, and re-enter the US with my H-1B visa?

General question: Is it possible to visit the US on the VWP, leave briefly, and re-enter on a different status (e.g. H, F, J, K, etc), without ever returning to one's home country?

I have posted this in Travel rather than Expatriates because, although in my specific case I have an H-1B visa, my question is more generally about VWP and travel, and I believe that it is applicable to travellers with non-immigrant visas.

There's a similar question here, although that's about going to the US and before having the H-1B visa.

A:
Can I visit the USA as a VWP tourist immediately prior to entry on non-tourist visa?