You may find an HVLP sprayer gives you mixed results with BM Advanced and for that matter, any higher viscosity paint. Better quality sprayers that come with their own turbine have more robust capabilities as well as wider variety of tips/nozzles to handle thicker paints. More often than not, people end up thinning thick paints to get suitable finishes.
Alternatively you could consider tinted conversion varnish (what most new painted cabinets are painted with) or tinted lacquer (most new cabinets used to be painted with lacquer, but lighter colors can yellow over time) which are both easily sprayed from an HVLP sprayer with superior results. Downsides are both are very stinky and do take some practice.
To be honest, if you want to use the advanced, use a regular high pressure pump with a fine finish low pressure tip which will atomize the advanced and lay down very nicely. You should be able to rent a pump from a professional BM dealer, or any other paint store (maybe even home depot) and ask them for advice on best tip (FFLP210 or similar) for your application.
You can adjust the pressure down and really get quite a low amount of overspray. You can plastic off the kitchen easily with painters plastic to keep paint dust down. Either way, if you spray, you will have to cover everything and anything you don't want paint on or drifted on in the work area.
Whole lot of words there, but maybe something in there will be of value!
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for laminate, comes in colors
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