OK, so, a flat architecture would suggest more links on the homepage, not less. You're trying to reduce the number of clicks from the homepage to each piece of content, not increase it.
If there's good quality content on those pages that helps your sales team, leave it up! If it helps the sales team, then removing it will probably cost you sales, right? I'd stay away from nofollowing those links, and I'd stay away from using rel="canonical", since the way you mentioned using it isn't how it should be used.
Removing 9 links from the homepage won't do all that much for you IMO. I'm looking at your homepage now. I don't think you need to worry about removing internal links. I would recommend changing the links for "QuickBooks, Peachtree, Simply Accounting, MAS 90, MAS 200, and Line 50." Either remove the links and leave the text, OR a better solution would be to link them to an internal page on the site such as /quickbooks-pos-integration.html, and target those types of keywords. But definitely don't link to quickbooks.com's homepage, they don't need that link juice and it isn't valuable to visitors.
Taking a look at the link metrics for your site, you're at homepage PA 53 and DA 43, which isn't far off from the page 1 ranking sites. I think some link building would make you much more competitive for that keyword. You're currently on page 4 when I search for "POS software", and it's an internal page that's ranking, not your homepage. Get more links to your homepage using POS Software as the anchor text, and do it in a non-spammy way. That will help quite a bit I think.