With 4 days you have a lot of options, but the key is to hike up higher than you plan to camp. I left CO about 10 years ago and now live in WI, so I appreciate that acclimatization you will need! The key is to start low and camp a little higher each night. You can hike up high, as long as you descend to an elevation that is more comfortable. With a 4-day backpack/scouting trip I would schedule it this way:
Day 1: base camp at 8-9,000 ft. Scout trailheads and do short hikes up ridges to glass and get eyes on the territory.
Day 2: Start a 2 night loop in one of your prime areas of interest. Camp at ~9,000 ft
Day 3: Camp at up to 10,500, but be flexible based on what your body says. You may be fine going higher, but you may need to stay lower too.
Day 4: wrap up the trip, maybe scout some access points on your way out.
I generally never had problems with bugs in CO unless I was near a marshy area. I've backpacked several times with just a tarp on ground. Your Seek Cimarron will be just fine.
As for weather, it can change on a dime. I normally just get a local forecast, but
https://www.mountain-forecast.com/ may be a good resource. Keep in mind, weather varies from one side of the mountain to the other. In the mountains, if you don't like the weather, wait ten minutes. If you still don't like it, drive 10 miles!