Please help! HVAC Nightmare

I am at a loss at what to do so any help would be greatly appreciated. On 1/28 I had carrier heat pump and air handler 37MURAQ48AA3 & 45MUAAQ48XX3 installed. a Honeywell Home Pro series was installed the system kept kicking in and off and not keeping the temp, a week in I checked my electric bills excited to see a big drop in usage/costs from my old system. I was shocked to see that I was being charged $50-70 a day and knew it must of been on aux heat 100%. The installer said the Honeywell was faulty, removed it and put an Eccobee on And I thought great since these are highly efficient. I had no heat the next day, installer came out, heat started working, then it was in aux heat 100% time again, installer came out and couldn’t get it to stop calling for aux heat so turned aux heat off. installer comes back next day and removes Ecobee and puts a wired remote controller on. I cannot see if the system is in aux heat. my electric bills are still high, higher usage then my old system (I compared) for example $25.00 day on mild days 30 degrees and my house temp is set at 65. I have no idea what the system is doing, it goes on and off randomly. The installer now says that my ductwork is the problem, which I have checked out and it does need some work however I had the same ductwork with my old 14yr old system (2 stage 5 ton frigidaire heat pump and Air Handler. The installer said he will remove the equipment and refund me which is great but I have no idea what to replace with!!! The system I had looked great on paper - cold climate energy efficient, EER2 10, Seer2 16, HSPF2 8.5

my house is about 1,800 sq ft. 1960s build so insulation is plaster walls, duct work leaky. But again this was all like that with the old system. Also, the old system was a 5 ton. There was a 20’ x 20’ room addition and the previous owners had tapped into duct supply truck and ran (4) 6” flex to addition crawl space for heat (no return)

I need to decide what to do because with the current system running as is my electric bill is $3k since install

greatly appreciate any help!!! thank you in advance