I don't know - the only cases I've encountered have been
after the event - ie when when an official body
took a long time in acting, and the complainant drew this to the attention of the Ombudsman, who investigated and either upheld or dismissed the complaint - I've not encountered a situation where the Ombudsman was effectively put into the position of intervening in an
ongoing case. And certainly their considerations are forensically thorough, so I wouldn't expect a particularly speedy result - certainly not on the timescale you have in mind.
I'd certainly take it up with the Ombudsman, on principle, and with a view to gaining some recompense, but since time is of the essence, I'd also pursue the UKVisas complaints procedure - details
here