Recorded Preliminary Round
San Francisco Symphony just sent out a message saying that their committee has opted to do a recorded preliminary round in February, with semis and finals in April for their Section Viola audition. As far as I'm aware, this is a novel approach to have a time-limited recording period, and one that I hope other organizations emulate to respect the time and financial constraints of applicants.
Below is from their message to applicants:
Here is how the Recording-Only Preliminary Round will function:
Candidates will receive the preliminary round repertoire list at 12pm (Noon) PST on Tuesday, February 24.
Candidates will have until 12pm (Noon) PST on Thursday, February 26 to submit their recording.
The recordings must be done in one take and in the order of the list with no editing.

It probably doesn’t go against any written rule. In my experience, the practice of number drawing is facilitated by whoever is proctoring the audition, and it’s down to that person to do it in an unbiased way, or not. I would say having candidates maintain the same order from round to round, and then plugging in a preadvanced candidate as number 1 in the finals is decidedly NOT the fairest way to do it.
I would recommend that any round that includes preadvanced candidates in it should have a completely new numbers drawn. I’ve taken some auditions that use numbers for prelims and then letters for semis, so as not to confuse the committee and inadvertently favor a player because they are the same number as a candidate who advanced from prelims. All final rounds I’ve ever played, screened or unscreened, have began with all the candidates drawing numbers out of a hat or a bag. This is the most transparent way - having proctors predetermine the numbers is just an invitation for doubts about fairness and favoritism. I would also recommend that phones be taken, either from the candidates or the committee members (or both), before the numbers are drawn for a screened round.
I do think it’s acceptable for the proctor to determine numbers for prelims, based on the order that candidates arrive. Most ensembles assign you to a certain hour, and when you check in they tell you which number you are. I don’t think it’s a good idea to assign prelim numbers before check in, because of A) possible discrepancies in warmup time and more importantly B) it’s just too easy for candidates to share their numbers with members of the committee in advance, if they have a relationship.