Dropping your chainring tooth count would help, and get you into the 12t cog more often. My concern would be the 32t cassette cog, it's on the smallish side to help with climbing for just about any practical chain ring you'd want.
You might want to also consider a different cassette. To get better climbing than the 12-32t you'd need to go with something like a 11-42t or 11-50t.
ModernBIKE.com has an 11-42t for $30.
Of course, going with an 11-42t cassette justs compounds the issue of not using the smallest cog now. I suspect you're going to need to need to go with a smaller chain ring as well so that should avoid this problem. What chain ring? Sheldon Brown's
GEAR CALCULATOR can shed some light on this. Input your small & large cassette cogs, chain ring, preferred cadence, and some bike specifics and see what impact this has on your speed. Lower speeds = less effort of course.
There's also Grin Tech's
MOTOR SIMULATOR that models the performance of various motors with variables for route slope, total weight, rider power contribution, etc. Lots of variables, but gearing is a complicated issue.
You mentioned chain length. Good point. It's hard to say if you'll need to make a change. Part of it is knowing how close your current chain is to the 'correct length' and the rest is your choice of final gearing. This
PARK TOOL article and video is one of many free tutorials they offer, this one focuses on getting your chain length correct. Frankly, it is likely you'll need to make a change to be sure you can climb that last block home.
Hope this helps.