Understanding that projectors are 100% for after dark viewing as a requirement.
Screen size will play a major factor in whatever you purchase and could alter any recommendation significantly.
ALL quality projectors, like those from Epson, BenQ, etc. will produce a bright image with very good colors without any real problem. So, that's not a major concern IMO.
If you have any specific placement requirements, that will be something of a consideration.
Overall, a great general recommendation is the Epson 3800. It has great placement flexibility and very good brightness with solid colors.
I think your speaker bar is a major issue. Speaker bars are generally bad. They are an improvement over integrated television audio, but they still tend to use small speakers and tend not to get very filling for a indoor space. In an outdoor space, it is likely to sound very thin with no bass impact. As well, they often lack the proper inputs on them to work with any device that doesn't have audio return channel or digital optical audio connectivity. This WILL be a problem because 99% of projectors don't have ARC or digital audio connectivity. This is something which can be managed by using a sound bar with HDMI inputs, or just by getting a HDMI audio extractor. The HDMI audio extractor is only about 30 bucks or so from Amazon.https://www.amazon.com/J-Tech-Digital-Extractor-Passthrough-JTD18G-H5CH/dp/B074HHSJVN/ref=sr_1_1_sspa
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.