What kind of screen are you using? The screen size is on the large side of things, but a projector like the 5050UB would be a bit brighter, but most home theater models just don't reach much beyond the 1,500 lumen range post calibration, which can be difficult on screens larger than 135" diagonal. Still, with a positive gain screen, it can help things out a lot.

The LG itself is a fairly bright projector with over 1,500 lumens in standard mode with medium lamp settings. That's quite bright and it won't be easy to find any home theater models which really get a lot brighter at this time.

I'm not sure what your room conditions are, but in a fully darkened room, this projector shouldn't have any issues at all, and buying something new would more likely be a sideways move in terms of brightness, or a somewhat negative direction in terms of image quality, shadow detail, and contrast.

https://www.projectorcentral.com/LG-CineBeam-HU810PW-Laser-Projector-Review.htm

The very solid models like the Epson LS12000, Sony XW5000ES, or JVC NP5 models are all really great, but they still are only peaking out around 1,500 lumens in brightness...
https://www.projectorcentral.com/Epson-Pro-Cinema-LS12000-Laser-Projector-Review.htm

This leads me to believe that either the screen is not delivering the gain structure you need for that size, or there are other issues within the room which aren't ideal for your setup which is where I would look at things first.

I love the idea of ever brighter projectors, but the hit to image quality is always a possibility which is why there really aren't any really bright models in the budget at this time. People do still keep waiting for a standout model to come along, it just isn't here yet.

I may be getting a bit out of my depth on this one, and I would suggest you ask the same question at AVS Forum as there will be more people than me with some answers that can help you out, and they will be more prompt in their responses. I just don't know of which models may be brighter and offer you similar, or better, image quality with that added brightness and stay within budget.

I do believe that you should be able to find some solution considering your very solid budget.

The screen is a bit of a question mark to me and remains so, and will be brought into question for sure. Not sure your room conditions, or how things look overall. The Slate screen is a ambient light rejecting material (ALR) and is designed for long throw projectors. It requires the lens to screen distance to be AT LEAST 1.5x the width of the screen away, which is certainly possible with what you have. But, it could be closer, which would mean the screen itself is rejecting light from the projector, which would be bad.

I'm NOT a fan of long throw ALR screens as they do a lot of harm to the image. They introduce sparkling and hot spotting issues. But, they can be important in the right room, with the proper setup.

Would love to see a photo of the room it is in, and ask if you really need a screen which rejects ambient light for most of your viewing or not.