It does sound like the problem is the secondary opening. You didn't mention what lighter spring you are now using, but here are some things to consider. First, let's make sure the diaphragm is actually functional. Vacuum leaks are common with secondary diaphragms that have been disassembled. A quick test is to remove the diaphragm housing from the carb and push the plunger in to collapse the spring. Then hold your finger over the outlet hole. This hole should have a small cork seal that seals it to the carb main body. If you hold your finger over the hole and release the fully collapsed diaphragm, it should stay in place. If the diaphragm spring slowly pushes the plunger out, you have a vacuum leak in the diaphragm, and it will not open under wide-open throttle. Generally, the leak is around the diaphragm. Usually, one of the little cover screws snags the thin rubber diaphragm and tears it. This will cause a leak. Or, the diaphragm is not seated flat in the housing and there's a leak.
The best way to fix this is to lay the diaphragm flat on the lower portion of the two-piece housing and use two fingers to firmly hold the plunger in place. Then install the cover with the spring (start with a purple spring-that's one step lighter than the plain spring). Carefully compress the spring while holding the diaphragm plunger in place. Then start all the cover screws by hand with the cover as flat as possible. If you feel a snag, back the screw out and reposition the diaphragm until all the screws are finger tight on the cover. Then tighten all the screws while you continue to hold the plunger up into the cover. Only release the plunger after all the screws are fully secured. Then test your work to ensure the diaphragm is sealed. You might also try removing the little steel ball that Holley includes in the vacuum circuit. Sometimes the secondary will open more quickly when the ball is removed.
Another thing to keep in mind is that this 5.3L is basically a 326ci engine-it's not very big. Plus, you have a heavy car with a 2.73 gear. Because your engine is so small, it won't have a lot of torque to begin with, even in First gear.
The other variable is the ignition. You mentioned chips, so it sounds like you have the Edelbrock system (PN 7118) that uses different chips to establish a timing curve. This system dials it in so you should be close. If the engine runs OK (doesn't surge or buck or sneeze through the carburetor) in acceleration but is just slow, I think the problem is more related to a leaking vacuum diaphragm. Fix the leak, fatten the carb up a little, and it will probably make this a much more lively combination.
You also mentioned breather-system problems. This is becoming an issue with the Gen III engines. It may stem from the rather small crankcase area built into these engines as compared with the older Gen I small-blocks with much more area. Blow-by can become difficult to manage at higher engine speeds because of this lack of crankcase volume. GM even bored holes in the main web bulkheads on the LS6 engine in an attempt to reduce the crankcase pressure fluctuations. Look for a place where you can increase the external vent area to atmosphere. It may require several stages of oil separators to accomplish this task. We know of one carbureted LS1 that used a breather plumbed right off the floor of the lifter valley. At higher engine speeds, it threw oil right out of the breather, so this is a problem with the Gen III engines.
A typical positive crankcase ventilation (PCV) system connects engine vacuum from the carburetor or manifold to a PCV valve that meters a given amount of crankcase fumes into the carb to be burned at idle or part-throttle. For this to work, you must have a vent to atmosphere on the other side of the engine. Stock engines pull filtered air from the air cleaner, while many car crafters merely install a filtered breather on the opposite valve cover from the PCV valve. Given your engine is a smaller 5.3L, it should be fine with the PCV valve system just described.