I don't hate you at all!
That was a well thought out answer to a nigh-impossible question. It does, however, require significant nationalization efforts to make it possible. Could they be made to merge? Yes. Would they do do willingly? That, in my view, is a definite no.
True that-but I think the premise of any consolidation plan is that the companies would not have made the same mergers willingly to begin with, or else they would have already done so. The hump to get over with any proposed plan of consolidation, imo, is the mechanism to induce those mergers. A couple of ways (not in order of likelihood, or anything other than the order they occur to me) are:
1) The conditions for the end of federal control. If you want to spin this off the butterflies of a TR 3rd term TL, it might work. Post WWI was a reaction/rollback of much Progressive policy. If TR is still around, there could possibly be a clause returning control of the RR's to their owners only to newly formed (and, again, a federal charter may be the key here) corporations that will own/control the grouped lines pending a final merger. That final merger could be mandated to occur within, say five years, under terms reviewed by the ICC. You will probably need another clause giving the ICC power to singlehandedly set the terms if no agreement is reached by that time.
2) The industry was-not exactly starved-but in need of much capital after WWI and the markets were less friendly to RR stocks/bonds for much of the 1920's. RR revenues were down so returns were not as attractive to investors, especially with other industries (automobiles being one) offering new opportunities. Again, I cannot see any direct aid going to the RR's during otl's conservative Republican administrations (and Congress); nor would a progressive/Democratic administration/Congress. You have a couple of options here, though. There were proposals floating around for a revolving loan fund to be financed by collecting part of the dividends that were paid by stronger roads,
over a certain limit.
This would be used to help finance borrowing by weaker roads. Again, only feasible if you have a stronger Progressive influence. If not, then-as I have mentioned before-the Hoover administration may offer some sort of loan program later in the 1920's. In either case, make these assistances available
only to railroads that are consolidated under the Plan.
3) The Great Depression, and much more federally based help is available but only to Plan railroads.
4) if you can get one or two companies formed and operating, the rest may decide to come along, rather than be left out.
No guarantees, a few butterflies needed, many released...but
not quite bat territory just yet, imo.
And, a disclaimer, as always-this is just about the initial set up, taking us to no later than 1942, when WWII puts everything into a cocked hat.