Sometimes I practice the arpeggios without the pedal but it is rather difficult to do this at speed.
No it isn't! Just let your fingers do what they're already doing, but don't put your foot on the pedal. It's one less thing to do--it ought to be easier! Of course it won't sound as good
(maybe that's what you really meant), but it will mean that you can hear clearly what your fingers are doing.
OK, I'm being a little bit harsh there. If you're used to using a lot of pedal, then it does feel strange to play without any at all. It takes a bit of mental adjustment, but it's well worth getting used to.
And I do have problems with tempo control but my hearing is corrupted and I only notice the fluctuations when I listen to my recordings, which is quite disturbing as well as time consuming.
It's OK, this actually isn't unusual. Recording and listening to yourself is exactly the right thing to do (even though the process is a little painful)--try to do this at least a couple of times per week.
To improve the rhythmic evenness, have you tried practising sections of the piece with variations? e.g. all staccato (without pedal of course), or with dotted rhythms?