I think that's a bit too high of a burden of proof in this case. We have the numbers for the Union army when it crossed the Rapidan and we know how many casualties they suffered; we have the numbers for the Confederate army and we know how many casualties it suffered. For the Union army (on the field as a whole, not just those making the assault) to be "merely" 50% stronger than the Confederate army, given known Confederate casualties just at the Wilderness, then we would need:
Confederates post-Wilderness = 55,000 (66,140 minus 11,033)
150% of 55,000 is 82,500
Union infantry corps at start of Wilderness= ~120,000
~16,000 Wilderness casualties, so ~104,000 left
Difference = 21,500
Essentially, for the Union army to be down to just 150% of the Confederate one, we'd need the Union to have suffered 21,500 casualties at Spotsylvania before the Mule Shoe assault and the Confederates to have suffered nil. (If the Confederates suffered 2,000 casualties before the Mule Shoe then we need to up the number the Union needs to have suffered by 3,000.)
I simply don't find that plausible, indeed I don't see how it can possibly happen, not when the casualties at Spotsylvania as a whole for the Union were the (already high) 18,400. This is why I believe it to be the case that the Union army had nearly or actually twice as many men on the field as a whole, which is our first approximation for the force ratio at the Angle.
As noted above, it's not, really; it's just assuming that they suffered casualties roughly in proportion with the rest of the Union army. A few thousand one way or another doesn't materially affect the conclusion, either.
Without exact numbers of the Mule Shoe, that is, the exact number in all the divisions engaged, north and south, we can't compare the man-to-man fighting ability. You made your point, which is that the Union army, as a whole, was much larger than the Confederate army as a whole, but that does not get down to the nitty gritty of how many individual soldiers were engaged at the actual mule shoe, and this is tough to take into account given the casualties that took place during the Wilderness and in the rest of the fighting leading up to the Mule Shoe.
It may be that the Unionists far outnumbered the Confederates, or it may be some degree less, even parity. We don't know. I assume the best grounds for parity would be if the Union divisions took heavy casualties beforehand, and the Union divisions were already small, by Confederate standards, at least compared to the ANV.
So without the exact numbers the issue is moot. It may be interesting to find out the exact numbers engaged at the Mule Shoe on May 12, but like I said I only know of Rhea possibly being able to help me, and I don't feel like flipping through his book for something that doesn't exist, given that I've never read it and am not sure what he's talking about.