You've got a good start on these pieces. Just a few friendly notes:
I would do the cresc in the first few bars a little more gradually -- the second chord kind of sticks out.
In the opening few pages, I could use more dynamic range. Also, make sure the D major measure of bar 42 is LOUD. Don't just blow past it -- it's a high point, but come way down in volume in the next few bars, but then look out, because there's huge cresc going into 46. Overall, more dynamic contrast...
The section starting on 63 is overall too loud. That section should be played as leggiero and soft as possible. Then again, it could be the piano you're using, I dunno...
I like the swell you do on the solo section on the next page meas 83-84, but the melody line is most important here, and I'm hearing a bit more concentration on the accompaniment than is necessary. Same goes for the next page when the melody is octaved. The melody needs to sing, so you might want to practice the solo sections of this movement (melody only -- no accomp) and try to get a good singing tone, then play it the same way when you add the other parts.
In measures 133 till the end of the page, less LH and voice the quarter notes in the RH more.
141, start even softer, the forte doesn't happen until 145. Again, it could just be the piano.
A bit softer starting at 153, then at 159 - 160 don't use any pedal and bring out the G-F-Eb-D-C in the LH.
193 till end of section, bring out quarter notes a bit more and watch that the accents on every RH set of octaves. Really accent the first octave, but not the following ones.
I know what you mean about the Alla marcia section. That's not an easy section to play. Just be patient with it.

139 till end of section is a lot slower than you were playing the previous section. It's marked Un poco meno mosso, but it should be a little less motion from what you were playing earlier, not from the previous 2 measures. It just needs to flow a bit more. This is also not an easy spot.
I lose the beat on measures 355 and 359. You do a good crescendo there, but put a bit more of an accent on the note that the LH plays when it crosses over, to solidify the beat.
One more thing, I'd start the accel. a bit earlier than you do on the last page.
There has been a lot of hype in Hollywood about Rach's 3rd concerto being so difficult in recent years, but if you ask me (I played this concerto 2 years ago), his 2nd concerto is every bit as difficult in spots. You're doing an excellent job on it so far, so keep it up!
