You might look into the Rimrock unit, it has pretty good access. But you won't be alone and in some places it can get steep. 
Rimrock for ML is permit only so don't go there.
Since you have hunted around Ellensburg I would go hunt GMU 340. If you have a quad or dirt bike or if you can borrow one this GMU would give you the most access. There are alot of ORV trails that you could use to get into areas that you normally wouldn't be able to access.. A word of caution though, you can't take a dirt bike or 4-Wheeler on any of the main roads. You have to stick to the trails. There's also alot of elk in GMU 340.
If you want to hunt the Yakima herd I would go to either GMU 360 Bethel or 352 Nile. There isn't very many guys that hunt it during the ML season and has a good amount of road access. This area could depend on the weather but there's a good amount of elk there as well.
GMU 368 is a really good place to ML hunt for spikes with good road access but this IMHO is THE most crowded place during the ML season.