What I'm not seeing addressed specifically in the thread is can the KW term within your H1 & Title differ? I get that if the whole title and whole header differ slightly like:

Title: Best Plumber Local |100% Satisfaction Guaranteed!

H1: Best Plumber Local offers 100% Satisfaction Guarantees!

*Please note - not my best copywriting effort at play here

Then it's not worth sweating over, so long as the searcher does't experience a disconnect between he SERP result and and the landing page messaging.

My concern is over the need to target "ugly" KWs - terms that don't fit well in to the UX equation, but have exponentially more search volume than they "prettier" version.  Let's say "plumber local" has 1,000 monthly searches vs "local plumber" that has 300 monthly searches. But "local plumber" is much better for copy/user readability.  Can you use:

Title for the SERP: Best Plumber Local |100% Satisfaction Guaranteed!

H1 for UX: Best Local Plumber offers 100% Satisfaction Guarantees!

...and still be nicely optimized for "plumber local" assuming you can find a smooth way to work it into copy (easier than doing it in an H1), alt tag, and site has otherwise good authority/reputation. Also, ugly KW (plumber local) would be used in the url).

Thanks is advance!