TL;DR- 7000 lumens workable but still not quite enough for outdoor daytime use
I echo the above comment about no projector being perfect for outdoors even in the shade without a five digit price tag.
I've been modifying my outdoor setup for at least a decade, and am finally where I feel like I can just use it rather than think of ways to improve it, the last piece being how can I use it earlier in the day. I have identical mounts both in the garage and on the front porch, where I project onto a brick wall, which isn't nearly as bad as I thought it would be. For a long time, I used a 2000lumen Panasonic PT-AX100, but late dusk was about as early as I could go, and even then it wasn't great. I now have a 7000 lumen Christie LX700 face melter that I found on ebay for about $550 plus another $100 for a short throw lens. It's about 27lbs, and only 720p which doesn't matter on a brick wall, but I can fire it up a lot earlier. The Panasonic was useless during the day at all times/locations, but the Christie is perfect in the garage on a cloudless day with the door wide open and sunlight reflecting off of windshields. Even 7000 lumens isnt enough for the porch on a sunny day, even though its ceiling mounted and the entire porch is shaded including the wall. I can make out an image but not gonna invite the neighborhood over to watch the game. It's passable all day on a cloudy day, but still not great. Good news is it becomes worthwhile maybe around 5pm, which was good enough for my needs.
The one big thing to share from what I've learned as a non A/V expert (and barely a hobbyist) is that the harder it is to set up, the less often it gets used. I started off needing to set everything up, table for the projector, portable amp, portable speakers, plus whatever source, so I only did it for special occasions. My satisfaction with this whole set up peaked when I got the identical mounts, a Denon dual zone HDMI receiver plus 4 outdoor speakers from craigslist, and a harmony remote/hub. Now if I'm in the garage I hit one button on the harmony just like I'm in the living room. To move to the porch I just move the projector and hit a different button, and takedown just means hanging it back in the garage. Now we go out there just to flip channels or stream stuff if it's a nice night.
I spent a long time learning about heavy duty projectors, settled on a few, then set ebay alerts until I found one of them with low hours that came out of a college building getting overhauled. Took about 6 months, but I wasn't in a hurry
(chrome won't let me make a link so you'll have to cut/paste)