We've done the Rose & Crown/Illuminations thing quite a few times and this is what we've learned; if Illuminations is scheduled for 9pm, which I think on most nights it is, I would get reservations for 6:30 and arrive at least 15 minutes before your ps. I think this increases your chances of getting a good patio seat. Then, take your time and order appetizers right through dessert. Of course, I'd also recommend tipping your server extra because you will be taking up his/her table for quite a while and let them know your not in a hurry. Don't order dinner until your appetizer has arrived. This should drag things out.
You cannot request a patio seat and whatever table is available when it's your turn, is the one that you get. We've always lucked out and been seated on the patio, except for our January trip. It was only my husband and myself and the concierge had made our ps and he did note a patio request. We arrived pretty close to 7pm and had about a 15 minute wait. The first table that came up was inside the restaurant. I wouldn't have minded, expect it was a table where one person sits on a bench and the other person gets the chair across from you, I hate those kinds of tables. We declined and were told that our name would go back into the queue for the next available. Well another 15 or 20 minutes later and we did get a patio table, but it was well under the awning. Unfortunately, we missed all of the aerial fireworks. My favorite part is the music, so I didn't mind too much, but even patio won't guarantee you an unobstructed view. You can always eat in the pub, which is a lot of fun and then step outside and to the right of the building to view Illuminations.