Hit & Run vs Morale Tests?

How do Morale tests and Hit & Run interact?

Hit & Run;
-happens at the END of an Assault Phase
-prevents Sweeping Advance rolls

Morale Tests;
-happen before sweeping advance, before end of combat pile in, therefore DURING the Assault Phase

So, in order, you would:
-determine assault results
-check morale
-hit & run (because a successful hit & run prevents sweeping advance)
-sweeping advance
right?

Does this mean a unit that FAILS morale Falls Back before using Hit & Run, therefore disallowing them from using Hit & Run at all because they are no longer locked in combat?
Or
Do they not suffer any penalties of morale tests at all?

Came up in a game the other day; my Haemonculus killed a Crisis Suit 1" away from Tau table edge, winning combat by 2. The Tau player then Hit & Run his surviving suits out of the combat. Should he have made a morale test or no? And if he did, could he have fallen back off the table?

I believe relevant rules are on p.26-27, 29, and 38. Dakkadakka is so far of the opinion that the H&R happens AFTER assault results/morale tests. I guess my biggest issue is the wording of "No Sweeping Advance rolls are made." They say that's in reference to the unit leaving combat at that point, not in reference to a failed morale test. How is it supposed to work?
Thanks for your time & help!

Hit and Run occurs after the assault phase. You do the assault completely normally, then afterwards if there is a unit with hit and run in combat that wants to use the rule to leave then it can.

In your example, the Tau player should have made a morale check, if he failed you can attempt to sweep (either catching and wiping him out, or he would get away but run of the board). If he was successful, at the end of the assault phase, after all assaults are done, then he can attempt to hit and run out of combat.

The reference to "no sweeping advance moves" doesn't negate the normal sweeping advance for losing a combat and failing a morale check, its simply stating that while using hit and run sweeping advances can't be used to catch them. A unit that looses a combat and fails a morale check is not using hit and run, it is fleeing, sweep away.