I think the main reason why Brownlow gets pushed down in the order companied to Dodger is because he doesn't sing anything.

I hve just finished directing a version of this for local am dram Company it was very well taken andi had th curtain call like this (reasons in brackets)

Adult Ensemble
Ensemble Soloists (they get solos therefore deserve that little mention)
Boys and girls
The Sowerberrys,
Mrs. Bedwin, Dr. Grimwig, Mr. Brownlow
Bumble and Corney (i put them here ahead Of bedwin and co as they have their own song and in our version they had a reprise in the second act)
Bet (she has a small lead part)
Sykes (And Bullsye! always good as he gets booed and just adds to the atmosphre of the show which is great)
Dodger, Oliver (they come on together as they are children!!! if it was a full adult show you would put doger lower and oliver higher but as they are children they enter stage together singer consider yourself, also it' a good point nt to put Childrn last for a curtain call as they forget to count for thier entrance so it helps if there is two of them and an adult cast member there to remind them)
Fagin,Nancy (I had thm enter coming on together singing I'd do anything as oliver and Doger join Bet to sing in our own rewritten verse for the end)

i then Had Bet and nancy with Sykes take a second bow followed by fagin with his gang(with dodger next to Fagin) and then Oliver takes the final Bow

In my school's show I play Oliver and the ending of the curtain call goes...

~Billy Sikes
~Oliver
~Dodger
~Nancy
~Fagin

Our director says this is the order the prompt has in pertaining to amount of lines and singing.. But I didn't see any such list in the prompt.

I like Salome's order but would offer the following adjustments, Nancy, Fagin, and Oliver should all have individual bows.

Ensemble
Fagins Gang
Dr. Grimwig/Mrs. Bedwin/Old Sally
Charlotte/Noah
Mr & mrs. Sowerberry
Dodger & Bet
Mr. Bumble/Mrs. Corney/Mr. Brownlow
Skyes
Nancy
Fagin
Oliver