I'd let her sleep Deb... I asked the exact same question before and that was the advice given to me!! Let us know how it goes.
Green007, with the set naps, you pick a time that's doable so maybe 11am on a wu of 5am or earlier as you've been getting. Problem is, you'll need to try and stick to a 12hr day as close as possible to her 'normal' early wu. For us, her WU's were 5.30-6, I'd get out of bed around 6.15-6.30, set nap at 11.30 BT at 6.15 with a view to being asleep at 6.30. The idea is to go by their 'get out of bed time' rather than actual wake time. There was a bit of OT for us in the beginning, but that soon went away. Then even with an early wu of 6, I had to start pushing the set nap later as we were getting 1.5hr nap or less at the original 11.30 time. And as I've just learned, anything more than 4.5hrs to bed here means OT. Preferably 4hrs.
With a 4am wu though, I'd probably do as deb recommended.. Really short am nap of around 15mins around 7.30-8 to get you close to your set nap time. Before O wouldn't do short am,long pm.. We just got two short ones. Now, however, I can let her have 10 mins in the car (I try not to put her to bed as I'd be encouraging a nap iykwim), then she'd be able to do until her set nap time or 15 mins later. Then I can do BT at the set time. O wouldn't normally sleep in the car like that, but if I time it right especially after an early wu, she will go off.
Hth. It's a rough ride, but I was sooo hacked off with the inconsistency of it all rather than anything else, that's why we went for the set nap route. I think it's worked in our favour tbh. As long as she wasn't OT before bed it was ok. the longer I pushed her in the am, the longer nap we got. But that might not be the same for everyone.