This part of the circuit doesn't show much to see your problem.

It does show the 2 coils in series eg 1B and EE. If they both had the same resistance, each would only receive half the voltage and fail to operate. As you say EE is 2 ohms and 1B etc are probably lower resistance than most other coils.

The 1B etc coils won't operate with a 20 ohm EE coil but you can do a quick test by shorting out the EE coil and very quickly bridging the rollover contacts, as in brush the bridge wire past the contact so the 1B coil can't heat up.

See if the 1B etc coils operate and latch.

I assume the scoring is added when either of the  1B etc coils operate, so, it could be done by the EE contacts ( not shown here). Just reread you post and it says off 1 contact.

"the EE relay does energize but cant get the sequence bank relays to energize" this may be due to EE energising too slowly due to the high resistance.

Andy