Solar inverter installation

The simplest question can have the most complex answer at times. I'll try to help. Variable speed systems have some advantages over single stage or single speed systems. For Florida I would say the best benefit is that it allows the system to be optimized for dehumidification in cooling. The fan slows down and the cooling coil gets colder and pulls more moisture from the air. This adds to comfort as well as reducing the risk of mold growth in the conditioned part of the home. If any heat pump system is properly sized for cooling it will almost certainly provide all the heat you need without strip heat to supplement. There is another choice which is 2-stage or 2-speed. In this case the high speed is reserved for the dog days and the unit will run on low on cooler days and in the evening. This may be a good choice. Reputable manufacturers will warranty their compressors for 10 years and I recommend Carrier, Trane and York as top brands. Be sure you save your purchase documents and register the installation. The most important thing I can add is that it's true that you get what you pay for. If you look for the lowest cost you get not only the lowest cost equipment but also a contractor perhaps less trained, less equipped and willing to cut corners that will affect you for years. It is my belief that when you see bad reviews it is more likely the contractor earning the score and not the equipment. So I recommend you pick your contractor first and allow them to customize the system to your needs.

The fridge motor is probably smaller than you think, the vacuum motor is a universal (AC/DC) motor so it inherently soft starts. The pump motor is likely a standard AC single phase motor and has too much inrush current for your inverter. When they say 1500W at start and 750W running, that's "marketing" speak because they don't want to scare people off. Starting an AC motor results in the inrush current being 500-600% of FLC for a second or two. But the power factor is very very low (i.e. .2 or less), so if you express it in "watts" the number looks better because W = A x V x PF. So 750W is about 1HP and at 115V single phase, that's about 16A FLC. That means at startup it can surge to 96A, but if the PF is 0.13, the W will be 1500 which LOOKS better than saying the starting current is 96A. For a utility connection it's irrelevant but for something powered by an inverter, it's too much and the inverter has a crowbar circuit that shuts it down to avoid damaging the transistors. Your best option (besides the generator one) quite honestly is going to be to get a different pump, either one powered by a DC motor that you run directly off of the battery (look for "solar pumps") or one that uses it's own inverter because that will come with soft starting. Or get a MUCH bigger inverter.