I've been developing in Magento for several years, and I can tell you without a doubt that it's better to keep the H1 tag wrapped around the actual product name on your product pages. This should be default on all pages except the home page, where the H1 is wrapped around the IMG ALT for the logo in the header. I prefer to move the H1 on the main page so that it wraps actual relevant text, but it requires a little bit of editing of the Magento core, and like everyone has said, heading hierarchy doesn't count for much in Google's algorithm these days.
The best way to add specific keywords for product-level pages in Magento is via the Short Description, General Description, and the Product Tags. Tags are likely the most effective solution, as this functionality was designed for customers to make notes about products, so "White Business Shirt" would look natural there and make perfect sense.
You might also try very minimal internal linking from your homepage if you have a specific product you're attempting to boost your SERP ranking for. Something like "Our best selling < a h r e f = product url >business shirt< / a >."
To be honest, there's so many factors involved in correctly optimizing a Magento-based site, I'd recommend not wasting your time with H tags at all, especially masking and duplicating them.
You'll be much better off if you concentrate on optimizing your category hierarchy, writing unique product descriptions, dealing with duplicate content, configuring robot instructions, decreasing load times, etc...
Plenty to do... no need to mess w/ the H1 tag.
Hope this helps & good luck!
-Anthony