I think you put your finger on the problem. You need a 25^F temperature drop across the evaporator to have aggressive humidity control with both stages. This will get your <50%RH during significant cooling loads. During evenings and rainy days with +55^F outdoor dew points and adequate fresh air changes to have a pollutant free home with optimum oxygen levels, plus moister producing occupants, you need +4 lbs. of supplemental dehumidification per hour.
Pass this along to your tech. Measuring air flow is difficult, follow by measuring the coil temperature and the supply temp/%RH/dew point as a final check on air flow. After you decide the temperature and %RH that you want the a/c to maintain, adjust the temp/dew point that the coil supplies at the grill. If want 75^F, 50%RH, a 55^F dew point in the home, target the dew point of the air from the evaporator at a minimum of 5^F lower than the return air from the home. For this condition, go for a <50^F supply dew point. These setting will remove +-3 lbs. of moisture per ton per hour of cooling. Keep in mind, on/off cooling may not remove any moisture.
Evenings and rainy days during the mild seasons of the year will have day time high evening outdoor dew points, yet a healthy home needs an fresh air change in 3-4 hours as per ASHRAE/American Medical Ass. to purge indoor air pollutants and renew oxygen for health and comfort when occupied. Keep in mind that most recommend eliminating fresh air as the first fix for high humidity in a home. Even leaking homes need supplemental fresh filtered air during the mild temps/calm wind seasons.
Always check the a/c supply for a +5^F reduction in dew point after any service or install to assure the a/c's setup/function is correct. It is comparable to taking the pulse of a person for life.
Now we have an a/c that should maintain <50% during significant cooling by removing 3 lbs. of moisture per ton, per hour of sensible cooling, if not now is the time to find where all the extra moisture is coming from. Bring on the blower door and duct testing.
The next challenge is to decide if we want a healthy and comfortable home during calm days, evenings, rainy days, and occupancy. If yes, provide mechanical fresh, filtered air circulated throughout the home with supplemental dehumidification to maintain <50%RH to provide comfort and control of the various biological growths high humidity causes. The most practical method is adequately sized whole house dehumidifier with the filtered fresh air option. Units like the Santa Fe Ultra, Broan, Trane, etc are ideal for this application.
Enough, keep us posted on what you do or additional issues with your contractors.
Regards Teddy Bear