Welcome to the forum Andrew. We're a pretty small site, and I don't think we have any snowshoe experts yet.
I don't really have much experience, but I can recommend a few things. I have a pair of wood snowshoes that have an equally annoying rubber binding. I did a little research myself and found what's called a "Lampwick Binding". I haven't had the chance to try it out yet, but it seems like the way to go for traditional style snowshoes. There seems to be several variations that come up on searches
My antique snowshoes
I did a quick google search and found this:
Lampwick Binding -
http://www.wildernessrhythms.com/1304
If you're looking for a more modern snowshoe, I really like the
MSR EVO Ascent snowshoes. These are very popular snowshoes around here. You'll seem them used a lot by mountaineers and guide services. I will be buy these at some point.
A couple really nice things about the MSR Evo snowshoes
binding style
the bindings open up completely allowing for large boots. You just step on and quickly latch the rubber bindings. Easy to do with gloves on.
Unibody Traction
MSR EVO snowshoes have long steel tractions rails instead of a small crampon at the ball of your foot on most modern snowshoes. This gives you great traction in a wide variety of conditions.
Floatation Tails
If you need additional floatation, just slap on the floatation tails!
Televators
The "Ascent" models of MSR snowshoes come with the televators which lock into place and lift your heel. This provides extra traction and reduces fatigue on steep ascents.
If the EVO Ascents are too expensive, they also have less expensive "Trek" and "Explore" models that lack the Televators and have different binding styles. At some point I'd like to find the time to do a thorough write up on these snowshoes. Check out the MSR website.
http://cascadedesigns.com/msr/snowshoes/category
And regarding the Snowtrek snowshoes, I'm not familiar with them, but they seem to be pretty average snowshoes. I suspect they would work just fine for mostly flat ground snowshoeing.
Please come back and share a trip report! Good Luck!