No, if anything it would be to little fuel pressure.
When troubleshooting gasoline powered carbureted engines there is a process that must be followed. And that process must be done in a certain order or else mistakes can be made. Each test is a simple pass or fail, either the test passes or it fails. The process goes like this.
1. Check compression
2. Check ignition timing
3. Check firing order (this is usually correct unless somebody was playing with the plug wires)
4. Check the fuel quality/run the engine off of a different fuel supply.
5. Check fuel pressure, it must be 3 to 7 psi at all times
6. check for vacuum leaks in the intake manifold
7. Rebuild or replace the carb.
So far we are at step #5. Fuel pressure can be low for other reasons besides a bad fuel pump. But either way, the engine will either have good fuel pressure, and you move on to #6, or it won't, and you have to figure out why.
If fuel pressure does end up being good then you move on to checking the intake for vacuum leaks. The easiest way to do this is to get some 6 in 1 foaming spray oil, you can get this from an Evinrude dealer or a Motorcycle dealer. This type of oil is like a WD40 but it foams up like shaving cream when you spray it. What you do is run the engine and spray the base of the carb as well as the intake to cylinder head gaskets and see if the oil gets sucked in or not. If it does, there is a leak.
If no leaks are found, and if all tests have been a pass to this point, then the problem is in the carb. It is either still dirty, or it's bad. Carburetors are a wear and tear item and they do wear out and go bad over time. The biggest issue with the carb is finding somebody qualified to rebuild it. Solex downdraft carbs are not a common carburetor, and only mechanics who have been around more than 20-25 years understand how they work. If the carb has been rebuilt by somebody qualified to do the work, and if it's still spitting gas out of the carb, then the carb would be replaced. What happens with carbs over time is they will start to leak internally. Fuel will start to leech through the metal over time and get into air passageways. This causes the carb not to be able to flow fuel correctly through it. Does that all make sense.