Recently tried to upgrade my DSL connection from a 6MB to a 16MB with Teksavvy. A tech came by today and told me there was no space on the remote to connect me so "tough luck" (he was actually pleasant to deal with). What I have noticed is that now when I run Speedtest I get 2.5MB down, when I was with Bell I was getting 5MB down.

While I have no proof (not that it would matter) when I moved from Bell to Teksavvy it would appear they kicked me off the remote and moved me to the CO and now that I want the faster service and need to get back on the remote, Bell is having none of it. Teksavvy's answer is that they can issue me a refund. I don't want a refund, I want a 16MB connection which Bell's and Teksavvy's site say I am capable of getting. Who wants to bet Bell will find space in the remote for a Bell customer?

I spent some time looking into it and this seems to be a common side effect of leaving Bell for a TPIA and it appears there is nothing you can do other than crawl back to Bell or go with Cable (where available). Feeling a little disgusted tonight.

Teksavvy has to escalate it - Bell shouldn't have accepted the order if the remotes are full.

You're likely on the default 3meg profile = 2.5Mbps real world.
Your line likely supports the full 5-6Mbps you got before, it just has to be bumped back up at the CO (again, ask TSI for it if Bell still says no room on remote and you drop back to 6meg).