What screen for high ambient light room?

Hi Guys and Gals,
There is no way I can totally darken my media room. It started out life as the music room until I decided to switch over to a projector. It is contiguous with other rooms that have widows. Viewing is compromised until after dark so I have to watch my formula one races in the light. I am using a Stewart Grayhawk screen 113" diagonal and the projector is a JVC DLA RS20. I will switch to a laser projector when the prices come down. What would be the best screen choices for my situation?
What’s your current projector lend to screen distance? What picture mode are you in? Is it bright enough? 
Model in mind high gain screen reduce black levels, so you want it as low as possible while still being bright enough (and of course ALR screens are more fun icky with figuring this out).

Distance is 18 feet. What ever normal is. I am an encyclopedia of Hi Fi information and the reciprocal when it comes to video.  

What ever normal is.
Go into the settings and see which you are on:
Cinema 1, Cinema 2, Cinema 3, Natural, Stage, Dynamic, User 1, User 2, THX

Is it bright enough? If you go on the remote and select Cinema 2 and then THX, how does they look (brightness and color wise)?
We are professional home theater designers and you have several major problems

1: JVC projectors are low lumin projectors

2: You have ambient light spill over

3: Your Grayhawk does improve contrast but is vastly inferior to ambient light blocking screens.

An ambient light reflecting screen will help as well as switching to a much higher lumen output projector you should be looking at a projector with 2500-3,000 lumins, most of the JVC projectors are 1,800 lumins

There are also DIY retrofitable battery powered blinds by Lutron

Have you considered a drape you can slide accross the room's opening to stop the light spillage?

Dave and Troy
Audio Doctor NJ
We Already have a black out blind in the most offending window but there is spillage around it. I suspect there are better. A laser projector will fix the lumin problem. The ones I have looked at are all 3000 lumins. I think the drape would push my wife a bit far plus most of our casual watching is done from the kitchen. We generally sit down to watch movies at night.
I certainly could fit a better black out drape. I think the easiest thing to do is change the screen. Is there a particular screen you like best in this situation?
Online calc says you get about 14fL of brightness currently, good for low ambient light, bright for a dark room.

A 1.1 gain would yield 17fL, not a huge difference, and at the expense of black levels, unless getting ALR.

With the Optoma UHZ65 laser projector with the same size/distance/gain, you would get  >23fL, and the calculator states good for rooms with ambient light.
Accept that with light spillage you still need an ALR screen to compensate for any light in the room.

OP please contact us we sell many brands of screens and we are sure we can find one that will be perfect for you.

Dave and Troy
Audio Doctor NJ Screen Innovations dealer
Very happy with the Da-Lite Parallax. Not a cheap option, but if you pull up the videos on their website, it's the real deal.