Nottingham (an English yeast strain) is known for it's very clean fermentation, particularly at lower temperatures. While you can some mellow esters in the upper 60s, it's forte is at lower temps for clean and almost lagery ferments. I like Nottingham, especially throughout the winter when I can put a fermenter in my garage with a blanket wrapped around it to keep in in the mid- to upper-50s. I'll use it through the spring in my basement where I can keep it up into the low 60s. After that, I put it away for 6 months until cool temps return.
I agree with the above posters that if you want a yeast strain that says "English" character then you might have been better off with a different strain (S04 is quick and flocs well but can potentially give unwanted character above mid-60s; WLP002 is another great English strain that will leave you with clear beer very quickly and just a touch of British esters).
Regardless, that's all well and good. Try to keep your nottingham around mid-60s for speed. Much higher and you might not like the results, much lower and it might take too long. Crash cool your fermenter when you've hit FG and you should be good with your choice. It'll probably stay a little cloudy but if the beer is darkish then it might not matter too much.
Forget using wine/champagne yeast. It won't help speed anything up, and probably won't do anything at all besides waste a couple bucks. Wine/champagne yeasts are suited for simple sugars. Maltose is not a simple sugar. While some simple sugars are created during a mash or found in extract, those sugars are the first consumed by brewers yeast so adding wine yeast towards the end is pointless. The sugars hardest for even beer brewers yeast to consume are what's left at the end of a fermentation - wine yeast won't know what to do with these.
Your best bet is to ferment with your nottingham in mid-60s for about 3-4 days, then let the temp rise to upper-60s for the remainder (2 days maybe), then crash cool for 3 days to drop as much yeast as possible. You might consider adding properly hydrated gelatin to the fermenter to aid in clarifying. This will put you at about 4+2+3, 9 days total. Burst carb for 24 hours at 30 psi with
light agitation the first 3-4 minutes (your beer should already be really cold from crash cooling so it'll absorb the co2 fairly quickly). After 24 hours, vent the headspace in the keg, and put on serving pressure. Pull 3-4 pints to get to the clearer beer and you should be set.
You're timeline is really cutting it. I highly doubt you'll have very clear beer but who cares, as long as it tastes good. Serve it in red dixie cups and you're golden
