I agree. Daniel's installed two units in March for us. One in the lanai and one in the master. The unit outside handles both inside units. We absolutely love them.

The lanai is closed in but has acrylic windows instead of glass!

Consider running additional duct work off primary unit
 

We had an enclosed lanai BUT it was "conditioned" by having two vents added to the existing AC duct work. I thought the electric bill was still fine. We even kept the doors to the main house open. We only had to close those main doors a few times during the year on very hot or very cold days. We moved from that house and have an enclosed lanai and would just add additional duct work if we needed it. However, we just leave the doors open to the main house and the lanai stays comfortable.
My thought would be try the "leave the doors open" approach and see how that works. If still not comfortable, run ductwork (probably two vents would do it). The vents can be adjusted to allow for more or less air volume. I think the additional vents would not be cost prohibitive if you felt like a mini-split was necessary in the future. At least get the estimates.

We recently enclosed in our ~300 square foot lanai on a ~1900 square foot home. We definitely need to blow insultation above it, but I'm concerned that even with the ceiling insulated (a) the glass is single-pane (i.e. not insulated) and (b) we're adding over 15% conditioned space for our AC unit to cool. Regardless of whether or not we extended the two ducts from our living room and added vents in the lanai, we would be placing too heavy of a strain on our AC system.

Is that true? I'm curious as to what would cause more load on the AC: the added ducts or just leaving the doors to the lanai open? In either case, wouldn't the single-pane glass also be "leaking" cool air?

I'm struggling with this as the wife really wants "open living" (i.e. leaving the doors open) yet probably wouldn't like having a much higher electricity bill, our AC blowout, and/or lose years off the AC's normal serviceable life.

Update
 

We decided to close all the Lanai insulated sliders, leave ceiling fan on and set the Mr. Cool thermostat and open living room door. After running it normally, all was great for 2 days UNTIL the inside unit started dripping condensation…. I am suspecting a clogged condensation line. Is this a dyi project will someone with average skills ? What gives me pause is I can not locate the drain line OUTSIDE the house. The only thing that is in outside area is a 1/4” copper tube that goes no where…. I would think the drain line would be the larger 1/2” pvc line like the ac has.. (home built 1999)

We’ve had our 2 ton Mitsubishi mini split since 2016 and our bill didn’t change much.
Very efficient and quiet. We love it.

Our mini split condensate line is in the white pvc conduit that also encloses our A/C line set going up the wall and is visible at the bottom. I have seen them run into the top of a nearby gutter downspout as well. You’re right, most are white PVC.

thanks for the reply, I will take a look for the pump inside there.