I'm a pretty big guy myself, so I can offer my two cents.
I would suggest you just plan to visit in September, The river runs much lower then. The only 'alternative route' is much much more strenuous and I would not suggest it unless you want to spend a lot more time, hike where there's no trail, climb over a mountain range and wade through miles of beaver ponds. The actual Stampede Trail is the easiest route, but it's still not easy.
Not to be insensitive, but I'd have to concur with your assessment that the raft won't work for you. Last year a 350 lb man was stranded on the other side of the river and a girl attempted to rescue him with an Alpacka raft, and it was not able to support the weight.
Best of luck to you though, if you do decide to go. You might be interested to know that there is a large group of hikers (of varying levels of experience) that intend to do the trail next September. Mike Kramer is heading that up and anyone is welcome. He's posted about it on the Back to the Wild group on Facebook here: http://www.facebook.com/groups/131401956882740/
Right now I'm currently working to shed some unwanted pounds (quite a few of them actually) in preparation for summer hiking. When there's something out there to motivate you that's so tangible as a destination like the bus, it really helps.
One last thing (sorry for the bad news) but the cable tram across the river has been down for some years now. There is hope that it will be repaired at some point, but it could still be years out, or may never happen.
Anyway, again, I really do wish you the best of luck. Be Safe!
Erik Halfacre - Moderator