This is an interesting surprise. I've added a pair of images tightly cropped to show the genitalia. Indeed the two "packages" look similar. Do you have an image of the female genitalia to link to here for comparison?
There were many Physocephala individuals in the meadow that day, drawn to a patch of Narrowleaf Mountain Mint, but for sure this is the same pair in all images. My first image of the stacked pair was at 11:12 am and the parting of the ways was at 11:27. That's 15 minutes. They were not "tussling" but appeared to be courting before the third image. Perhaps something else is documented here, but it had none of the characteristics of two males battling it out. If indeed the bottom fly is a male, why is he posing like the female in this image:
In any case, the last crop apparently shows an intentional superimposition of the genitals.

To answer your first question, each thumbnail below shows a female P. tibialis with a discernible theca, which is the flap (or nub) under the 5th sternite...situated well before the distal tip of the abdomen where the genitalia are:

       

Note that the theca in females of this species is fairly small, and I suppose it's plausible that the range of variation may be such that for some female P. tibialis it may be easy to mistake a very small theca for the absence of one. That situation is unlikely to occur in some of the other taxa in subfamily Conopinae, particularly in Physoconops, where most species have females with much larger thecas than in Physocephala...for instance, see below:

       

Next, regarding the the notion of a typical "mating posture (and positioning)": what that posture may be; and whether the pair in your images here...and the one in the thumbnail you referenced...are representative of such a typical posture — these are indeed interesting questions! But, in hindsight, I think I was way too cavalier in my comment here, where I presumed that post represented the typical "mating posture" for Physocephala.

In fact, prompted to reflect more deeply by your comments, I now think I was wrong when I presumed that the male curling his abdomen laterally around the side of the female's abdomen and placing the tip of his abdomen next to the females theca constituted typical "mating posture". I now see that this doesn't make sense...since the actual genitalia of both male and female(!) are located at the distal tip of the abdomen. The theca is simply an appendage the female uses to help pry open the tergites of a(n unfortunate) bee...into which she then forcibly inserts an egg (which subsequently hatches within the bee host and develops as an internal parasitoid). So fertilization would NOT be achieved by having a male hold the tip of his abdomen against the theca. Moreover, I can't really clearly discern the theca in any of those "male on top with curled abdomen" images anyway!

However, there are a number of posts which do look like a more plausible "mating posture (or position)"...where the genitalia (at the distal tips of the abdomens) do appear to be in contact AND, moreover, the female has her theca conspicuously extended and visible (thus unequivocally showing the presence of a female, rather than two males). See the posts below:

           

So I would like to herein formally retract the (cavalier) implication I made earlier (in my comment accompanying the thumbnail you referenced in your comment above) that the "male on top with curled abdomen" constitutes a "mating posture". Instead, I'd speculate that the posture seen in the 5 thumbnails I referenced directly above would be a more reasonable candidate for such a posture (that is assuming such a notion is even well-formulated...there may be many different effective mating postures employed by different pairs of P. tibialis...a la your Kama Sutra metaphor elsewhere :-).

The simple point behind my initial comment on your post here (and a number of other posts) is that one should not (again, cavalierly!) assume that whenever an image shows one individual on top of another, that the image is showing a mating pair! There are definitely posts (like yours) where two or more males are on top of one another...but in nearly all such posts, the tips of the abdomens can be seen not to be in contact...so reproductive mating is clearly not what is happening:

       

It could be that males sometimes pounce on other males and engage in tussling to try to drive away rivals.

And it may also be that males sometimes over-eagerly pounce on other males without an intent to "tussle", but from making a mistaken assumption that the "pounc-ee" is a female. And some may be so excited and single-minded that it takes them a good while to realize their mistake.

That either behavior (or a combination) would continue for 15 minutes does seem surprising to me. But, as the saying goes: "Stranger things are true!" I guess they may have been somehow triggered to engage in a kind of "courting behavior"...but that would be unlikely to have a favorable reproductive outcome, considering they're both males. Many other possible hypotheses could be put forth to explain the behavior here...so again, I don't think it necessarily follows this was some sort of "cryptic mating pair". It could have been they both got tired of struggling after about 3 minutes and then mostly gave it a rest for the next 12 minutes before throwing in the towel altogether :-)

Come to think of it, the "curling the tip of the abdomen" posture might be explained as the male below trying to raise his abdomen to be too high for the one on top to subdue. Or also as an attempt of the individual below to get some leverage in order to laterally push the individual on top off. That these two were engaged for so long could simply be a manifestation of the almost universal phenomenon in the animal world of persisting in doing something ineffective for a good deal of time simply because there is a deficit of intelligence to see that nothing is really accomplished by the present stubborn behavior, and it might be better to come up with an alternate behavior! :-) Sometimes we (animals) repeat mistakes over and over...seemingly interminably...before at last an inspiration arrives and it occurs to us to try a different way to go!