IF I understand you correctly:
Are you saying that you have to pump one shot into the intake and then it starts; but that without the shot it will not start, cuz that's the sense I am getting. So in effect you are expecting it to just spring to life when you twist the Key? Even EFI cars automaticaly send a shot into the intake under most conditions, AS YOU ARE TWISTING THE KEY.
A little further down you say
"it would kill trying to get it out of the yard"
Which leads me to believe that some to all, of the fuel in the bowl has evaporated. This cannot be solved by any carb overhaul so if I got this right, then don't blame your carburetor rebuilder. Instead, fixing boil-off or percolation, is a different issue.
Modern gasolines are made up of a bunch of other fuels all mixed together. Some of those fuels evaporate at as low as 95*F, others at over 400*. Your engine will not start on the 400 degree stuff, you just do not have enough heat of compression. There are a bunch of other fuels in there with in-between boiling points. If you park your vehicl in a plave where the carb is gonna see over 95*, that light fuel will be gone in a matter of hours. If the carb sees 120* other fuels will evaporate and eventually all you have left in the bowl is syrup, and the engine will not start on that. Meanwhile, the same thing is happening in your fuel tank, and the gas in the line is boiling and the gasses are moving to the high point, which is usually elbowing it's way thru the pump, and up into the fuel bowl, and out the vent into the atmosphere.
This action forces some of the fuel back to the tank. And when this is done, later, your pump will struggle to pull up fuel from the tank, and is gonna push a lot of non-liquid gas up into the bowl which is way more interested in escaping out the bowl-vent than going into your engine.
So then, there you sit pumping and cranking and hoping you'll have enough battery to get some actual combustible liquid-fuel into the fuel-bowl.
There is no cure for this using modern fuel ...... except
1) install an electric pusher pump at the back, and hit it every time the vehicle has been sitting even overnight. Let it fill the bowl and hope for the best.
2) seal the fuel tank to prevent evaporation. But if you do this you may require a hi-pressure relief to not blow your tank up, and or protection against the air pressure in the tank from blowing gas into your engine. This used to be handled by the charcoal canister and still is, but nowadays the canister is closer to the tank, is under the vehicle, and is electrically controlled by the EFI computer.
If your vehicle does not have a charcoal canister, you can easily retro-fit one. but you still need a non-venting gascap. That should solve the over-pressurization issue. But you still have no cure for the carb boiling dry. The low-pressure pump at the back is only a bandaid, and it works.
But since you say that not long ago, you did not have this issue, maybe something else is causing your carb to run hot.
If I had to guess I'd say, one or more of these may be a contributing factor;
1) your exhaust cross-over system, is malfunctioning and cooking the carb from below. That is the first place I'd look.
2) The second thing, is if the carb is sitting in a hot hot doghouse.
3) The third is if the cooling system can't keep a high-enough efficiency, and the engine is running hot., or the trans cooler is.
5) if the carb is sucking in hot underhood air, that's like a runaway nuclear reactor, hot to hotter to hottest.
4) remember; Every time you shut the engine off, heat rises and boils your gas.
5) Chassis problems such as; dragging brakes and low pressure tires, or the kayaks tied up on the roof., not to mention if you are simultaneously dragging something behind.
6) But, since you say that she is fine out on the open road, honestly I don't suspect any of these. So Just saying, and something to think about.
That's all I got.