The seven-year-old won all of his three hurdle races last season, with two victories coming at Cheltenham.
He relished the step up to three miles when impressively landing the Grade Two Albert Bartlett Novices' Hurdle at Prestbury Park in December 2021.
However, he subsequently suffered a setback and has been sidelined since.
A general 6/1 second favourite for the Stayers' Hurdle, Byrnes was hoping to see Blazing Khal run over Christmas, but has not been able to step up his work.
The son of Kalanisi was given a outing on the sands at Beale Strand on the Shannon Estuary, an hour's drive from the trainer's Ballingarry yard, on Sunday.
However, with a trip to the Dublin Racing Festival at Leopardstown on February 4 and 5 also ruled out for a belated return, Byrnes admits Blazing Khal's Cheltenham bid is "probably a long-shot".
He said: "We are hoping to get a run into him. Cheltenham is still very much in the balance. I would say it is 50-50 at best. We have stuck him in - the entries close tomorrow - but he will not run at the Dublin Festival, either.
"It is probably a long-shot now that he'll make it to Cheltenham. We are going to try to do our best, anyway. We had him on the beach yesterday, but we have to take baby steps with him. He's still not doing strong work."
Byrnes, who won the Stayers' Hurdle with Solwhit in 2013, will not entertain thoughts of going straight to Cheltenham without a prep run, either.
He added: "There is no way we'd go to Cheltenham without a run. But we are running very tight in time. There are a couple of options - there's a race at Gowran and a race at Navan after the Dublin Festival.
"But is all getting very tight now. Part of the problem is we don't really know what the problem is.
"He is not moving as well as we'd like him to, but he's going to be doing everything now - he's going to be given every chance, but it is probably 50-50 at best.
"He'll have entries at Punchestown and in France as well, but Cheltenham is looking tight. It is what it is, people have worse problems."