Been a while since I have perused this thread - mostly being "depressed" over the H1 being discontinued and worse the migration to the web-based management/programming interface over the "thick client" (which I still use and will continue until forced to move).
The Logitech remote replacements and web based services are a huge step backward as far as I am concerned and I have seen nothing or read nothing that changes that opinion.
As for the many H1 users that have the swollen battery condition, the best thing to do is figure some way of getting them out and replacing them with a proper model. For those that have not read through this lengthy thread, there are a few battery replacements being sold as an H1 replacement but that is not always the case.
Examine the specs on the old battery carefully against the one you want to buy. Besides the 3.7V rating the other important spec is the 950mAh value - some of the replacements being sold are 930 or lower and while it may not seem to be that big a deal these batteries do not last as long, some do not charge properly, and there were some that believed caused damage to their H1s (but that is suspect).
Spend the time and research the proper replacement and pay the price (around $12) over the lesser ones being offered up as replacements.
Here is a suggestion: