Are you having issues in Allard or Heritage Valley in SW Edmonton? You're talking about a fair sized area and being more specific as to where can help.Telus, Bell and Rogers all have towers roughly the same distance from Allard.
First thing you should consider is talk to tech support at Telus Mobility and ensure they are aware of the issue and your exact address. The more people that call in and report issues, the better picture they'll have of where the issue is and are more likely to invesigate. They will need multiple examples to rule out there just being an issue with one phone.
Getting new towers installed is not a fast or a cheap process. Especially if some area residents are off the mindset that they don't want a big tower next to their back yard. You can find more information on the process here: http://www.ic.gc.ca/eic/site/smt-gst.nsf/eng/h_sf11435.html
Part of the issue very possibly could be your phone as well. Some questions to better understand your situation:
Telus doesn’t disclose cellular expansion plans, so no one here knows.
I find Telus Wi-Fi calling service fills in gaps where no cell service is available. Check and see if it is available to your phone.
You can also look at this map to see which towers are line of sight to your location.
Ultimately, you have to choose what works best for you.