That is interesting since usually the slow tempos are hard accuracy wise. Faster tempo= smaller the gap between notes to make mistake
However 135 bpm for 8th isn't that slow . My guess is that your stroke technique itself is bit unstable yet.
It will be a tremendous help, especially if you don't have teacher.
Free stroke singles. This is the foundation. Get Dom Famularo's book ''It's Your Move'' or at least start to practice free stroke from those videos.
http://www.vicfirth.com/education/drumset/domfamularo/dom2HQ.html
http://www.vicfirth.com/education/drumset/domfamularo/dom4HQ.html
http://www.vicfirth.com/education/drumset/domfamularo.php
Also this was nice thread:
http://drummerworld.com/forums/showthread.php?t=18274
Practice those a lot, do the ''2-50'' exercise. Practice full strokes at the beggining then got to low and half strokes. They will probably be your main strokes.
Also before you can play decent free stroke, you could not use Beatnik. It will make you worry about timing when your main focus should be perfect form.
Yes
At the beginning use subdivision, later when you get more stable, go to tracking analyzer.
It's always good way to ask many questions, everyone is different and although things might sound simple, over internet it's hard to explain all the details. It's much better to ask three extra questionand get it right , rather then to keep silent and start to practice ineffectively.