Three things to check in this situation.

Are your prints fully developed (that is, are you developing by time rather than snatching the print when it looks right under the safelight)? Adox seems to recommend about one minute at room temperature for Neutol Eco at 1+9, but since prints are normally developed to completion (or virtually so), it will do no harm to try leaving your strips in the developer longer. Agitation is also recommended; if you're just leaving your strips lie, the developer in contact with the print emulsion may be locally exhausting, resulting in loss of blacks. I'm used to continually rocking the tray after putting the print in, since it's only for (in my case, with Dektol 1+2) two minutes.

Are you making contrast grade test strips and inspecting them under the same light you'll view the final print with? You apparently know how to do exposure test strips; a contrast strip is the same thing but with contrast filtration changing and exposure kept constant. I normally print split grade, so I'd use a wide strip or a whole sheet, and expose steps one way with the yellow filter (Grade 0 or 00) and then expose the other way with the magenta (grade 5). You're making your strips without a filter, so you're getting the equivalent of Grade 2 or 2 1/2; if your negatives are low contrast (which will typically scan well) you might need grade 3, 4, or even 5 to get full blacks with an exposure for the mid-tones.

Finally, are you doing the same with your exposure test strips (viewing in the same light you'll use for the final print)? I know you've said this doesn't matter here due to the extreme level of your problem, but I'll leave it here for completeness. Even Ansel Adams (re)discovered late in his career that a change in his inspection light changed his prints -- a brighter light causing him to print darker and bolder.

One of these should fix your "muddy prints" problem in terms of blacks.

Grayish whites, on the other hand, suggest fogged paper. Despite passing a safelight test, your paper could be age- or heat-fogged, possibly before you even received it. If you have the original box, it should have an expiration date on it; if you're years past that date, your paper may be age fogged. You can sometimes help this by adding a small amount (30-40 mg per liter) of benzotriazole to your developer, but that will tend to make the blacks problem worse instead of better. Try developing a sheet or strip fresh out of the box (remember, agitate and go two minutes instead of one) -- and take one sheet and fix it without developing. If they aren't the same level of white, you have fogged paper.

Honestly, the best solution for fogged paper is to either fix it out for alt-process use, or discard it and buy a fresh box.