I am not sure I concur on a drive-through crossing being automatically unacceptable to regulators - I think somewhat reasonable safety precautions could make it workable:
One crash, one breakdown, one puncture and the whole bridge could be logjammed for hours - with potentially dangerous overloading from the queue behind. A 30+ mile traffic jam on a bridge is unthinkable
I doubt it would be hours of the entire bridge logjammed, given it would likely be the most heavily monitored roadway in existance, would be provided with a hard shoulder as an escape lane and would likely be provided regular contraflow crossovers. You could even provide an extra normally-closed lane on the right hand side.
Given how hard access is to many motorway stretches, with no escape really feasible accept along the carriageway, I'm not sure an escape walkway and refuges at the base of bridge towers (where boats can pick up people in the case of a catastrophic fire) is beyond the pale.
The water is sufficiently shallow from a Formby launch that it would likely resemble a viaduct more than the Dartford Crossing, you would be capable of designing a bridge to survive the static loading of stationary nose-to-tail traffic
EDIT:
If you insist on a rail only crossing then you still won't carry significant numbers of unaccompanied trailers, since the business model will change given that even a slow 140km/h Shuttle train would have you from Southport to Ardglass in 90 minutes.
By the time you've messed around unloading your trailer and conducting formalities you would be on the road on the Irish side.
Once you include slack time on the receiving end given that you can't absolutely guarantee your receiving tractor and the trailer would be in the same place at the right time, I can't see it being worthwhile to bother with unloading the trailers and having them lifted twice, before being picked up by a different trailer. Especially with depatures every 15 minutes.
EDIT #2:
That's an extra cost you're imposing on the hauliers right there as the current Irish sea freight model is based almost exclusively on unaccompanied trailers: the cabs and drivers don't go on the ships, they drop their trailers and go (often picking up a return trailer on the way)
In 2019, according to the relevant DfT stats, only 55% (268k/484k) percent of good vehicle transits to the Republic of Ireland from GB ports were unaccompanied.
Which whilst a majority is hardly "almost exclusively", this suggests the economics of one model against the other is relatively finely balanced.
EDIT #3:
Worth noting that the 35km from Formby to HS2, is to
HS2 at the WCML. The closest point on HS2 is at the northern end of the Wigan branch as it joins the WCML.
So the HS2 connection is also a WCML connection, assuming we assume that the line is not going to be so full that an electric hauled freight going 75+mph is not going to get in the way between the bridge and Wigan.