Lager yeast to fix a stuck ferment

I brewed an American Wheat two months ago and had a stuck ferment at 1.020. I'm 99% sure it was an aeration problem so I roused the yeast (US-05) after 3 weeks hoping to kick start it with no luck. I pitched a new packet of US-05 four weeks ago and I'm still stuck at 1.020. A friend of mine suggested pitching a lager yeast to try and reach my desired 1.011. I will be pitching a starter of Wyeast Octoberfest (2633 I believe) that I started today once it's at high krausen.

My question for the forum is should I attempt to do this repitching at normal lagering temperatures or low to mid 60s?

Have you tried warming it to about 70F to see if that helps? If you do go the lager route, I would keep the temps up, your flavor profile is set, you're only trying to drive those last few points.

Was this an extract kit? DME or LME if so?

I raised the ferment temp up to 68 when I roused and repitched. I would have liked to get it in the low 70s but it wasn't possible. It was an all grain recipe my friend gave me based off of Three Floyd's Gumball Head.

How did your OG compare to your expected? Was your efficiency high enough to get down to 1.011? Could be you are just done unless it is tasting sweet.

My OG was 1.039 when I was shooting for 1.047.

My efficiency was around 55-60%. When I sampled my hydrometer reading today it still tasted sweet. I assumed that my beer should be able to ferment out to 1.011 and it was poor aeration causing the problems.

I pitched a 500mL starter of 2633 at 64^ last night. Woke up this morning and can see it slowly taking off. Hope this works because I really don't want a 2.5% super-session beer, haha.