The law changed in April 1862, giving the President a choice within a grade.
There is always seniority, even within officers appointed on the same date. McClellan ranked Fremont by these rules, because he had held a regular rank, whereas Fremont had only held California state rank. The rules were that for officers appointed to the same date of rank:
1. For regular officers, by seniority before the appointment. Serving regulars ranked all ex-regulars and volunteers.
2. For ex-regulars, by their relative seniority.
3. For pure volunteers, by order of complete legal appointment if members of the same corps.
4. For pure volunteers etc. of different corps, by lottery.
The President was free to set any date on the rank, and was free to issue a new Commission with a different date of rank. He did this with Hooker's volunteer Major-General commission, despite it being unnecessary since he was allowed to place junior officers over senior ones from April '62 onwards. However, the seniors weren't required to served as could simply resign their position, as Fremont did rather than serve under Pope.
Halleck would have been the choice to be the next General-in-Chief. To do this Lincoln would have to simply backdate Halleck's rank to the 14th May 1861. Halleck would rank Fremont by the Regulations (and would have ranked McClellan, his Captaincy being 1st May '47 vs 13th Sept '47 for McClellan).
However, it's more likely that Lincoln simply wouldn't have appointed a new GinC and Stanton's committee would be formed earlier.
In the Army of the Potomac, it was a longstanding objective of many in the party to restore McDowell to command. Banks was a volunteer major-general, and so McDowell would have to be raised to a regular major-general (since within a grade, regulars rank all volunteers). It seems likely that McDowell would thus ascend to command.
McDowell wanted to make a frontal assault against Centreville, and repeat Bull Run.
Sumner is out. He had a serious accident in December '61 and was expected to never return to service. It surprised everyone when he turned out to command his division in March, and he was still hobbled.
On 31st December '61, the command line is:
- MG McClellan (appointed 14th May and confirmed in rank 3rd August 1861)
- MG Fremont (appointed 1st July and confirmed 3rd August with rank backdated to 14th May)
- Acting* MG Halleck (appointed 19th August but not nominated to the Senate until 6th December. Rank not confirmed until 10th February 1862)
- Brevet MG Wool (not substantive until May, when the flash to bang of Lincoln's appointment to Senate confirmation is 2 days)?**
- MG(V) Dix (appointed 14th June and confirmed 3rd August, ranked Banks by dint of a former regular Commission)***
- MG(V) Banks (appointed 3rd June and confirmed in rank 3rd August 1861)
- MG(V) Butler (appointed 16th May but confirmed on 5th August, making him below Banks and Dix)****
- Acting MG(V) Hunter (appointed 13th August '61. There is no evidence of the rank ever being sent to the Senate I can find, although I assume it was)
- Acting MG(V) ED Morgan (governor of NY, appointed 28th September, nominated on 21st December and confirmed 15th April 1862)
- BG Harney (pre-war)
- BG Sumner (everything done in one day on 16th March '61, Sumner had accepted before appointment)
- BG Mansfield (appointed 18th May to rank from the 14th, confirmed 3rd August)
- BG McDowell (appointed 14th May, confirmed 3rd August)
- BG Anderson (appointed 17th June to rank from 15th May, confirmed 3rd August)
- BG Rosecrans (appointed 14th June to rank from 16th May, confirmed 3rd August)
- Acting BG Cooke (appointed 21st November to rank from the 12th, nominated 21st December and confirmed 7th March 1862)
* POTUS could appoint generals as he pleased, but there was a deadline for the Senate to confirm it. I think Halleck was about to run out the clock, and had Fort Henry not fallen, the Senate would have let his rank lapse. Something to consider for alt-hist. Need to check how long they had to confirm.
** As a brevet MG he ranked below all substantive MG's, regardless of seniority, but above all BG's. As a regular rank, MG would be above all MG(V)'s. I need to check whether brevet regular rank trumps volunteer rank.
*** Although the dates made Banks senior, Dix argued that due to a former Commission he should be senior, and this was accepted. The Army Register shows Banks then Dix, but be aware this was disputed.
**** Butler claimed seniority on the basis of first appointment, but seniority is sealed when POTUS signs the Commission after Senate approval, and the Senate decides dates. Up until that point you are only really acting in rank. The regulations came into effect as the dates were the same, and since Banks was confirmed two days before Butler, he was senior.