OK. First of all, let's solve the clues, or at least as many as I can do quickly.
ALEX CROSS 2012 action thriller film starring Tyler Perry as the title character (4,5)
AUTOCROSS Timed competition in which car drivers navigate a defined course one at a time (9)
CROSSBOWS Ranged weapons which fire bolts (9)
CROSSETTE Lateral extension in a corner of the architrave of a window or door (9)
CROSS-EYED Having one or both pupils turned inwards towards the nose (5-4)
CROSS-FADE Make a sound be heard gradually as another becomes silent (5-4)
CROSSFIRE Gunshots from two or more directions passing through the same area (9)
CROSSINGS Pelicans, toucans, puffins, and zebras, perhaps? (9)
CROSSNESS Irritability (9)
CROSS-PLAY The ability of gamers to use different consoles or platforms whilst online together (5-4)
CROSSWALK A marked part of a road where pedestrians have right of way (9)
CROSSWORD This puzzle! (9)
CUT ACROSS Go through (a place) to shorten one's route (3,6)
IRON CROSS Prussian military decoration established in 1813 (4,5)
MOTOCROSS Off-road race on two wheels (9)
RUN ACROSS Meet (somebody) by chance (3,6)
CROSS-CULTURAL? Associated with groups from diverse societal backgrounds or ways of life (5-8)
CROSS CYLINDER Ophthalmologists' tool developed by Edward Jackson to correct astigmatism (5,8)
CROSS-EXAMINED Questioned (e.g. a suspect) (5-8)
CROSS-PURPOSES Confusion or failure as a result of people working or talking with different goals (5-8)
DESIGNER CROSS? Hybrid dog, e.g. Labradoodle or Goldador (8,5)
LACROSSE STICK Piece of sports equipment comprising a roughly triangular net on the end of a pole (8,5)
SOUTHERN CROSS Symbol appearing on the flags of Australia, New Zealand, Brazil, Samoa, and Papua New Guinea (8,5)
WAY OF THE CROSS 'Via Crucis' (3,2,3,5)
We're missing a few, but maybe it'll be OK. Most notably, we don't yet have anything that would fit the long across space on the lower side on the right, with B in third place, and we have at least candidate solutions for all entries of that length, so something above is wrong. Let's proceed anyway.
(Fair warning: some things are indeed wrong at various points along the way, but I promise it all gets resolved in the end. I could have tidied it up and presented a nice clean solution path with no errors, but I prefer honesty.)
First note that
we have two 9(+4)s on the left with A in second place. Looks like these have to be LACROSSE STICK and WAY OF THE CROSS. Their second-last letters are C and E respectively; these have to be the second letters of two 9(+4)s that share a second-last letter. The C looks like it has to be CROSS CYLINDER, and the E looks like it will probably be DESIGNER CROSS or CROSS-EXAMINED.
None of that
can distinguish between across and down, since everything is symmetrical, so now let's look at the 5(+4) starting with A. That's probably ALEX CROSS or AUTOCROSS. Both of our candidates for the long word that intersects have T in sixth place, so this one looks like being AUTOCROSS. Coming down from the end of this we have a 5(+4) with A in third place; that looks like being CROSS-FADE or CROSSWALK. Hmm, figuring out which will have to depend on finding one of them somewhere else. Now, what about the long one meeting that? Looks like it has to be CROSS-EXAMINED. So its I is in the middle of a 5(+4) and the only candidate for that seems to be CROSSFIRE. Oh, and getting CROSS-EXAMINED means we've broken the across-down symmetry from the previous paragraph. Time to show the current state of play, all of which is still a bit uncertain because we haven't solved all the clues.
Next
it looks like what Qxw has helpfully numbered as 16a is CROSSINGS and 11a is CROSS-PLAY. 2d can't be AUTOCROSS so must be MOTOCROSS. 10a seems to be CROSSBOWS, CROSSWORD or IRON CROSS. CROSSBOWS could go with CROSSNESS in 1d; IRON CROSS would go with ALEX CROSS in 1d; CROSSWORD doesn't seem to fit any candidate for 1d.
At this point we should consider
what 9(+4)s we haven't entered yet. There's CROSS-CULTURAL (if it's right, which I doubt), CROSS-PURPOSES, SOUTHERN CROSS, and DESIGNER CROSS. Two share a beginning at top left (must be CROSS-CULTURAL and CROSS-PURPOSES). Two share an ending at bottom right (must be SOUTHERN CROSS and DESIGNER CROSS). And one of the sharing-an-ending ones must actually be wrong, so that we can fit that B in. SOUTHERN CROSS really isn't open to any doubt, so DESIGNER CROSS must be wrong. Ah, seeing that we're going to have L-B at the start it's obvious that the dog one is more specific than I'd been thinking: LABRADOR CROSS.
OK, so now
13a seems like it must be CROSSETTE. We seem to have some trouble with 4d; maybe MOTOCROSS is in the wrong place. But 19d sure seems like it has to be CROSS-FADE, resolving the uncertainty about 15d which must be CROSSWALK; and 19a must be CROSS-EYED. What's left at this point? ALEX CROSS, CROSSBOWS, CROSSNESS, CROSSWORD, CUT ACROSS, IRON CROSS, RUN ACROSS. We have to put CROSSBOWS and CROSSNESS at top left. Maybe time for another grid:
Nearly there.
12a is ALEX CROSS. 3d is IRON CROSS. 18d is CROSSWORD. And now we seem to have RUN ACROSS and CUT ACROSS for 17a (where either will fit) and 4d (where neither will fit). Ah, duh, we can put CUT ACROSS where MOTOCROSS is now, and then RUN ACROSS in 17a and MOTOCROSS in 4d.
The final grid:
