I'm not planning on doing anything any time soon, but in case anyone wants to run bots to see if this can be improved, this might help:
The "RNG" is located at address $A7, though as you can see in the trace log below, it is more like an entropy byte where the game increments $A7 over and over until the NMI next kicks in:
C341: 20 13 C1 JSR $C113 A:01 X:4C Y:00 SP:FD P:24 nvTbdIzc Cy:29375255 PPU-Cy:42199
C113: A9 01 LDA #$01 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375261 PPU-Cy:42217
C115: 85 51 STA $51 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375263 PPU-Cy:42223
C117: E6 A7 INC $A7 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375266 PPU-Cy:42232
C119: A5 51 LDA $51 A:01 X:4C Y:00 SP:FB P:A4 NvTbdIzc Cy:29375271 PPU-Cy:42247
C11B: D0 FA BNE $C117 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375274 PPU-Cy:42256
C117: E6 A7 INC $A7 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375277 PPU-Cy:42265
C119: A5 51 LDA $51 A:01 X:4C Y:00 SP:FB P:A4 NvTbdIzc Cy:29375282 PPU-Cy:42280
C11B: D0 FA BNE $C117 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375285 PPU-Cy:42289
C117: E6 A7 INC $A7 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375288 PPU-Cy:42298
C119: A5 51 LDA $51 A:01 X:4C Y:00 SP:FB P:A4 NvTbdIzc Cy:29375293 PPU-Cy:42313
C11B: D0 FA BNE $C117 A:01 X:4C Y:00 SP:FB P:24 nvTbdIzc Cy:29375296 PPU-Cy:42322
That explains why inputs (specifically directional inputs) can change the "RNG".
How the address $A7 is used to get the delay when drawing the next number (which ranges from 0x1E=30 to 0x2D=45), which is stored in $7010:
B1BC: A5 A7 LDA $A7 A:00 X:20 Y:00 SP:FB P:26 nvTbdIZc Cy:29999266 PPU-Cy:38061
B1BE: 29 0F AND #$0F A:6D X:20 Y:00 SP:FB P:24 nvTbdIzc Cy:29999269 PPU-Cy:38070
B1C0: 18 CLC A:0D X:20 Y:00 SP:FB P:24 nvTbdIzc Cy:29999271 PPU-Cy:38076
B1C1: 69 1E ADC #$1E A:0D X:20 Y:00 SP:FB P:24 nvTbdIzc Cy:29999273 PPU-Cy:38082
B1C3: 8D 10 70 STA $7010 A:2B X:20 Y:00 SP:FB P:24 nvTbdIzc Cy:29999275 PPU-Cy:38088
B1C6: 60 RTS A:2B X:20 Y:00 SP:FB P:24 nvTbdIzc Cy:29999279 PPU-Cy:38100
At the end of the delay, the game uses $A7 to determine the drawn number (essentially by mod 80) as follows:
B25B: A5 A7 LDA $A7 A:B2 X:5B Y:06 SP:FB P:A4 NvTbdIzc Cy:32887155 PPU-Cy:35602
B25D: C9 50 CMP #$50 A:FD X:5B Y:06 SP:FB P:A4 NvTbdIzc Cy:32887158 PPU-Cy:35611
B25F: 90 05 BCC $B266 A:FD X:5B Y:06 SP:FB P:A5 NvTbdIzC Cy:32887160 PPU-Cy:35617
B261: E9 50 SBC #$50 A:FD X:5B Y:06 SP:FB P:A5 NvTbdIzC Cy:32887162 PPU-Cy:35623
B263: 4C 5D B2 JMP $B25D A:AD X:5B Y:06 SP:FB P:A5 NvTbdIzC Cy:32887164 PPU-Cy:35629
B25D: C9 50 CMP #$50 A:AD X:5B Y:06 SP:FB P:A5 NvTbdIzC Cy:32887167 PPU-Cy:35638
B25F: 90 05 BCC $B266 A:AD X:5B Y:06 SP:FB P:25 nvTbdIzC Cy:32887169 PPU-Cy:35644
B261: E9 50 SBC #$50 A:AD X:5B Y:06 SP:FB P:25 nvTbdIzC Cy:32887171 PPU-Cy:35650
B263: 4C 5D B2 JMP $B25D A:5D X:5B Y:06 SP:FB P:65 nVTbdIzC Cy:32887173 PPU-Cy:35656
B25D: C9 50 CMP #$50 A:5D X:5B Y:06 SP:FB P:65 nVTbdIzC Cy:32887176 PPU-Cy:35665
B25F: 90 05 BCC $B266 A:5D X:5B Y:06 SP:FB P:65 nVTbdIzC Cy:32887178 PPU-Cy:35671
B261: E9 50 SBC #$50 A:5D X:5B Y:06 SP:FB P:65 nVTbdIzC Cy:32887180 PPU-Cy:35677
B263: 4C 5D B2 JMP $B25D A:0D X:5B Y:06 SP:FB P:25 nvTbdIzC Cy:32887182 PPU-Cy:35683
B25D: C9 50 CMP #$50 A:0D X:5B Y:06 SP:FB P:25 nvTbdIzC Cy:32887185 PPU-Cy:35692
B25F: 90 05 BCC $B266 A:0D X:5B Y:06 SP:FB P:A4 NvTbdIzc Cy:32887187 PPU-Cy:35698
B266: AA TAX A:0D X:5B Y:06 SP:FB P:A4 NvTbdIzc Cy:32887190 PPU-Cy:35707
B267: BD 00 75 LDA $7500,X * A:0D X:0D Y:06 SP:FB P:24 nvTbdIzc Cy:32887192 PPU-Cy:35713
B26A: F0 09 BEQ $B275 A:00 X:0D Y:06 SP:FB P:26 nvTbdIZc Cy:32887196 PPU-Cy:35725
B275: 86 22 STX $22 A:00 X:0D Y:06 SP:FB P:26 nvTbdIZc Cy:32887199 PPU-Cy:35734
B277: E8 INX A:00 X:0D Y:06 SP:FB P:26 nvTbdIZc Cy:32887202 PPU-Cy:35743
B278: 8A TXA A:00 X:0E Y:06 SP:FB P:24 nvTbdIzc Cy:32887204 PPU-Cy:35749
B279: 20 45 B2 JSR $B245 A:0E X:0E Y:06 SP:FB P:24 nvTbdIzc Cy:32887206 PPU-Cy:35755
However, if the number was already drawn, then instead of adding the drawn number, the game sets a random delay in $7010 (odd number from 1-15, based on the drawn number) then tries again after that delay:
B267: BD 00 75 LDA $7500,X * A:44 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078389 PPU-Cy:35644
B26A: F0 09 BEQ $B275 A:69 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078393 PPU-Cy:35656
B26C: 8A TXA A:69 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078395 PPU-Cy:35662
B26D: 29 0F AND #$0F A:44 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078397 PPU-Cy:35668
B26F: 09 01 ORA #$01 A:04 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078399 PPU-Cy:35674
B271: 8D 10 70 STA $7010 A:05 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078401 PPU-Cy:35680
B274: 60 RTS A:05 X:44 Y:06 SP:FB P:64 nVTbdIzc Cy:34078405 PPU-Cy:35692
That's all I found out.