Trying this with all proxied cards, because Innovation is more accessible after the move than Dominion:
3: BSCCE, buy R
4: SCCEE, buy S
5: CC(s)RSC, play R, buy R
6: BSCEE, play B, call R, buy RR
7: CCCE(s)B, buy R
8: RRRRS, play 4R, buy nothing
9: SCCCE, buy R
10: CE(s)CER, play R, buy nothing
11: RSSCC, play R, buy R
12: BSCCC, play B, call 6R, win.
Well, that RRRR draw was really lucky. I'll shuffle better this time?
3: BCCCE, buy R
4: SCCCE, buy R
5: CE(s)RCC, play R, buy S
6: RBCEE, play R, play B, call RR, buy RR
7: SCCC(s)E, buy R
8: RRCCE, play 2R, buy nothing
9: RRCCE, play 2R, buy nothing
10: BS(s)RCE, play R, play B, call RR, buy RB
11: SCCCC, buy R
12: EECC(s)C, buy nothing
13: RBBCC, play R, buy nothing
14: RSCCE, play R, buy B
15: RS(s)CCE, play R, buy nothing
16: BBSCC, call 6R, win.
Unforced error in bold, I could have called just R to buy RB, and this would have been over on 13.
3: SCCCE, buy R
4: CCCEE, buy S
5: BC(s)SCE, play B, buy R
6: CCCEE, buy nothing (two silvers ought to be enough)
7: RSCC(s)R, play RR, buy B
8: BCCEE, call RR, buy RR
9: SCCCE, buy R
10: (s)RRBCE, play RRB, call RR, buy RR
11: RCCCE, play R
12: RRSSE, play RR, buy B
13: BCCC(s)S, buy R
14: RCCCE, play R
15: RRRBE, play RRRB, call 7R, win.
The fact that you can play and call RCs on the same turn really gives this a chance to speed things up. However, I think you have to win the RC split here; five just doesn't cut it. If you get two 5s on T3/4 (as I did in the first game) then you're golden and might win by the end of the third shuffle.
I'm not an expert, but I'd call this a legit combo.