Can not get temp below 77

When you say creeping back to 78 are you meaning the set point temperature or the actual room temp creeps up???

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Drain the radiator, follow the top radiator hose to the engine, it is connected to the thermostat housing. Loosen and remove the two bolts, lift the housing and remove thermostat, make sure the new thermostat goes back in the exact same way, tighten bolts, make sure pepcock is closed on radiator, refill radiator, start engine, run heater on full blast, add coolant as needed.

If your unit is running 24/7 you are either low on charge or the unit is to small for your house.
A 20° temperature difference is about normal for the room air vs the air coming out of the ducts, but the room air and the leaving air should keep getting colder and colder.
An air conditioner should cycle approximately 3 maybe 4 times in an hour if it's properly sized.
As for the thermostat thermometer they are very cheap and are more for reference than actual temperature, so if 78° is not comfortable, then you should set it lower but not rely on thermostat being accurate or what the thermometer is saying as long as it is consistent.
The air conditioner and thermostat can also be set below 78°, there's a lot of people set them at 72° and below with no problems.
the only thing is if you have real low humidity you'll need to watch indoor coil or the suction line (the big line) on your outdoor unit and make sure it doesn't freeze up on you.

if it is set to 76 degrees and its 78 in the house its working fine it is suppose to shut off once it reaches 76 but sometimes there is a 1 or 2 degree differential built ini would keep you filter clean and as long as it blows out cold air i wouldnt be to concerned most airconditioners need yearly cleanings though

a/c will only bring temp down about 15 degrees from outdoor temp

it sounds like thermostat which tell unit to turnoff
and set the temp. you can test them with hair dyer buy putting it on heat see what dose then cool. The display should show the temp. if so then it should shut off or turn on is. If not could be a bad thermostat. Or is the thermostat in a hot spot in the house is should be near the return. Hope this helps. Yes I do for living Paul

If the space temp is (example) 72 degrees and you set at 80 degrees the unit should not come on. The A/C comes on when the space temp gets 2 degrees above setpoint temp. What type of tstat was installed digital or old syle mechanical. I'm leaning more towards a short in tstat wiring

the stat is in the upper rad hose follow the upper hose to the mtr the hose goes to the themostat housing there are two bolts holding it on look to the left of the housing you will see a sensor that is screwed into the intake manifold when you remove that sensor coolant will run out

go to nearest supply house or a good hardware store buy a themometer in the domestic ref, temp range. then compare it to read out.question is you house at 77 degrees. no way will domestic side have such an instant change in reading, the walls of the ref keep a long time fix on temp change.trust the themometer.

Is the heater staying on all the time? Most likely cause of themostat trouble is the sensor. Try to find it and measure its resistance at different temps to verify the trouble.