Nice diagram! There are many possible solutions. Here's one:

Perhaps this problem was too simple, and so the solutions make
up for that? The obvious solution--now that we've seen that
nice image of the rope problem--is to tie the swing lines to
the tire bridles with Double Becket Hitches. I'm assuming
that the image that was referenced is accurate not only in
the general need, but also fairly accurate in the physical
ANGLES of the two bridles (from the tire)--i.p., that they
form a fairly acute angle, less than 45deg!? Otherwise,
one might need to take some precaution to using the Becket
Hitch to bind the bridles, as the load would want to pry
open the hitch's turn around it. (One such precaution
would be to tie the apex of the bridle into a loopknot,
as suggested above--exactly the sort of thing done e.g.
on lobster pots, where the bridles on a set I've recently
checked form approx. 125deg. angles (wide; approx. equal
tension will be on each leg as is on the connecting line!).)

Incidentally, I'd been thinking about orienting the bridle
lines such that the center of them ran through the tire
and the ends were used for connecting; but this would put
bad lateral forces on the tire (unless one put mid-line
stoppers in for each hole), and in any case be going in
the too-clever-by-half direction. (-;
As for stoppers in the ends, recommend Ashley's Stopper
(which he misnamed "Oysterman's"): tie an overhand noose
(aka "slip-knot", but really it's not, but ...) in the
end; set the overhand knot pretty snug around the part
to be loaded (standing part); then tuck the end through
the noose and draw down upon it to lock. If you do it
correctly, you get a wonderful 3-pointed stopper face
offering good resistance.

Cheers,
--dl*
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