Kenny, what bike are you riding? I don't recall any squares in my 13x13 which I had to walk to get to. 14x14 is different though as it will go deep into the Pentlands.
Normally a Cervélo but for the trickier ones it would be a CX albeit still with slick tyres on it. I am considering resurrecting a MTB which has lived in a shed for 4 years and is not functional right now. Probably taking it in to Bicycle Works on Monday next week to see whether it's salvageable.
In terms of tiles, firstly my activity map is here:
https://veloviewer.com/athlete/554850/activities
The one which has Black Hill in it, which is 2 tiles north of West and East Kip, that doesn't look possible on a bike with slick tyres. Any further south look like they'd need a walk over the Pentlands, which is fine, I will aim to do a couple of them while summer is still here.
Then there's one south of Cauldhall Moor, which is 2 squares east of Howgate. Again, a bit of a walk to get to that one, I'd guess?