First off, does it have a new fuel filter, air filter, & did you check to make sure no mice built a nest inside the air cleaner? (When you replace the fuel filter use the proper sized wrench, make sure to put the fuel filter in the right way, & be very careful not to cross thread or overtighten it when you put it pack together... the carb is aluminum and many carbs (all brands) can be damaged easily because they are alum.
Sounds like there may be an electrical short possibly... what are the conditions outside when it acts up? (Temperatures, sunny/raining, etc).
Also, is the engine fully warmed up when it does this or cold?
Reman'd units are a gamble... some are done properly while others were seemingly taken apart, cleaned, bad bits replaced and slapped back together... seeing the mileage, its very likely it sat for a looong time and the carb is gummed up a little and just needs to be cleaned out. A Professional rebuild of that carb will pay off later as you upgrade the engine... Look up Sean Murphy Induction... they do a fantastic job & the price is very reasonable for what they do to your carb... costs about the same as a Reman'd but is 100x's better than Reman'd and anout 50x's better than stock.
First, Try running a full tank of Mobil/Exxon 93 through it... their fuel blends are of very high quality & have a lot of cleaners in them which should loosen and remove varnish, but if it persists, it may need to be professionally taken apart and cleaned... (I only use Mobil/Exxon in all of my vehicles unless I'm desperate for a fillup, get better mileage and never any problems with dirty fuel filters ).
Second, You "could" also shoot a few shots of carb cleaner into it (while running only), but you should have someone with experience helping... Too much carb cleaner will drown the engine, causing a stall, and it can wash the cylinders, leading to engine damage. Before you start, and after the air cleaner is off, look inside the carb to see what you are dealing with. There are 2 "Butterfly" valves... a small one at the front and a larger one in the back... the front is the Primary Fuel Metering Circuit: aka "Primaries" and is always pumping fuel when the engine is on. The larger one in the back, toward the firewall side, is the Secondary Fuel Metering Circuit: aka "Secondaries". This only operates when you push more forcefully on the gas pedal... the more you press, the wider it opens, until you reach Wide Open Throttle aka "WOT". The Primaries Sip fuel, while the Secondaries are the main cause of poor mileage because everytime you hammer the throttle, they open and let the engine guzzle fuel so it can rev higher and full to the floor is WOT... meaning you are wasting gas... ie learn to feather into the gas pedal.
Anyway, the proper method for using carb cleaner on your car would be to first put on safety glasses, remove the air cleaner, make sure nothing falls into the carb, and nothing is near it that could get sucked into the carb (it will suck a lot of air like a vacuum because an engine is just an air pump, hence vacuum lines, etc). Also make note where the vacuum line going from the carb to the air cleaner thermovac connects, start the engine (again, make sure no rags or papertowels are anywhere near the carb, & definately no smoking!). The safety glasses are very important because they will protect your eyes from any carb cleaner spray that gets whipped back at you from the engine's fan... it will & its not good if it get you in the eyes, trust me.
Stand on the drivers side of the engine and find the throttle on the side of the carb. Put your fingers on it and push it back gently to rev it slowly up a little bit.. then point the carb cleaner spray tube closely at the carb's front Primary butterflies. As you spray, rev it slightly higher to prevent the engine from stalling out . Lightly press on the button and Spray out a few shots (again, slowly) into the Primaries first: Small Butterfly at the front. Then go back to the Secondaries and do the same.. rev it enough to open the Secondaries slightly to get access... DO NOT Push the throttle all the way to WOT because you can damage the engine by over revving it with no load on it...(load being the car in gear and the engine working to turn the trans/driveshaft/axle and pushing the car.) The whole idea here is to gradually get enough carb cleaner into the carb over the period of a few minutes so it can eat at the deposits and work on them... again, too much carb cleaner shot in at once won't do any good. A lot of people make that mistake, rev too high and spray half a can into the carb, washing out the Cyls, & not doing much because it gets sucked past the problem before it gets a chance to work. Gradually spraying it in keeps the problem areas covered in the stuff and allows it to eat at deposits.
Check the electrical wires for any damage and also the electric choke to see if it is functioning properly. Mice LOVE to build nests on top of the intakes on these engines, so its not uncommon to find wires knawed on, which can short out and cause problems.
If you turn your car's ignition to the "ON" position (don't start it), you should hear a ticking sound coming from the carb.. This is an ECM test of the idle control solenoid which is moving the metering rods up and down repeatedly.... the ECM should do this every time the car is about to be started... if left alone in the ON position, it will tick about 30 times....
If you were willing to, you can do it yourself, but if you are not very mechanically inclined, it is a little complex and does require a few specialized tools that are getting tougher to find these days.