Oh, I love these "Running well according to shop and previous owner" breakdowns. There be Many Stories.
First off: How old is the gas in the carbs? If the gas in the carbs is more than 3 months old, the light ends have evaporated leaving behind the harder-to-burn heavier "ends". The accel. pump may squirt liquid, but it ain't flammable in the cylinder. It WILL catch on fire however, and melt the carb/car/garage down, so beware and have a wet towel nearby.
The best way to fire it up?
I'd change the oil FIRST, by dropping the Drain Plate and Screen and inspecting both them and as much of the inside of the engine as you can see with a strong flashlight. If everything appears to be intact and not growing Stalagtites or Stalagmites, replace drain plate and add FIVE quarts of 20w-50 conventional oil if the oil filter is currently empty. Adjust the valves and while there, check to see ifin there's any significant rust on the valve springs. If so, that's not a good sign and you might want to stop here and take the heads off.
Put in NEW plugs.
Then I'd get a can of Fresh Premium and fill the carbs with gas via a separate C/912 fuel pump that you can easily pump with your hand, and some 8-10 feet of fuel hose. Attach about 4 feet of hose to the Inlet of the C/912 fuel pump in your had, and put the other end of the line into a can of fresh gas. Attach another 4' length of hose on the Outlet of the fuel pump in your hand and stick the other end of that onto the Fuel Line going to the Carbs.
(If you want to drain the old gas from your tank, use the fuel pump on the ENGINE to pump the old gas out into a waste container or two, through yet another 4' of fuel line.. Two empty 5 gallon gas cans work well.)
Note: it really helps to have a TRANSPARENT fuel filter in the line going to the carbs so you can eyeball the gas's progress.)
With the C/912 fuel pump in your hand, YOU are now the "Fuel Pump" feeding the carbs!
Congratulations on the Promotion!
OK, so with the inlet end of the fabric fuel line below the surface of the fresh gasoline, operate the C/912 fuel pump by grabbing the flanges with your fingers and pumping the rod with the palm of your hand.
Think Isometrics. Exercise and Porsche debugging at the same time. Such a Deal.
When the carbs aren't yet full, the liquid surface in the fuel filter is violently disturbed with each stroke of the Fuel Pump. When the carbs are full, the surface will become Quiescent, and no more gas will be pumped. At this point, stop pumping!
With fresh gas filing the carbs, and fresh oil inside, and the valves adjusted and new spark plugs installed, and Spark Present, turn the key and...
If it STILL doesn't start. Let me know and we'll continue the debugging.
Keep the 356 Faith,
Maestro
P.S. Timing:
Remove Distributor Cap. Crank engine so that pulley TDC mark is aligned with Timing Mark on Case. (be sure Rotor ponts to #1 plug wire too!) Turn key to "On". Crank pulley a couple of inches COUNTERCLOCKWISE (to the Left), and then slowly but continuously CLOCKWISE (to the Right), towards TDC mark on Case. Eyeball the points for a little "spark". When you see a spark, STOP IMMEDIATELY! See where OT Mark on Pulley. Is. The OT mark notch should be about a 1/4" to the LEFT of the Mark in the Case. That's about 5 deg advance and a good place to start. Adjust if necessary.
After fire-up, adjust the High Speed Timing with a Magic Sears Timimg Light to, say, 33 degrees and see if the Idle Timing is between 2 ad 7 degrees. If so, your Distributor is pretty good.