Okay, let's take a few seconds and reflect on what you need to establish the flame and what you've actually got.
A.What you need:
1. You need gas at the proper pressure (3.5 IWC in the manifold whenever the main gas valve is open.
2. You need a solid pilot flame to ignite the gas when the main valve opens.
3. You need good flame propagation from the pilot to the first and subsequent burners (this needs to be almost instantaneous).
B. What you've got:
1. Gas at 3.5 IWC in the manifold.
2. Solid gas flame.
3. Light-off but not smooth and sometimes the pilot blows out.
From a comparison of what you need versus what you've got, I'd say flame propagation is your issue. Remember that water is a by-product of combustion and water creates rust. Rust not only deteriorates burners over time but also clogs the burner outlets.
Really old burners were made of cast iron with a lot of little holes for the gas. These units lasted many decades as cast iron resists rust quite well. Newer atmospheric burners switched to stamped steel tubes with louver type gas outlets. These louver type tubes can get very easily plugged with soot and I've seen many where the louvers were damaged or missing, thus allowing too much gas to enter the flame area.
Finally, when you advance to the fan assisted combustion, you get to the in-shot burners with their airplane like wings that are the crossover tubes. Those crossover tubes must also be kept clear of any rust and/or damage that would close them down. Cleaning crossover tubes should be part of any annual service but many techs don't even know they're present.
In summary, I believe your issue is a result of slow flame propagation leading to periodic sudden over pressures as the unignited gas accumulates and then ignites.
If YOU want change, YOU have to first change.
If you are waiting for the 'other guy' to change first, just remember, you're the 'other guy's' other guy. To continue to expect real change when you keep acting the same way as always, is folly. Won't happen. Real change will only happen when a majority of the people change the way they vote!
Sorry but you're out of sequence. Start with measuring your inlet pressure static, just the furnace then under full house load. Compare with the mfrs requirements for minimum inlet pressure, which is usually stated at 4.5wci but may be higher so don't assume. You'll usually get about 1"wci drop from inlet to manifold through the valve. If there is an obstruction in the gas piping or a problem with the medium pressure regulator at the meter or undersized gas piping, a manometer may not always reveal it. We just had this discussion a few weeks ago. Before changing a valve, always hold your hand loosely in front of the gas pipe and open it fully for just a moment. See if you hear any gurgling or feel debris fly out and hit your hand. You'd be surprised.
With the new valve installed, disconnect the supply tube either at the valve or where it enters the manifold before the orifices and attach a manometer. Read the true manifold pressure. Those pressure taps built into the valve can lie.
As for the pilot, disconnect it from the valve, remove the pilot orifice and blow the tubing out. Replace the pilot orifice as needed. Attach a manometer to the pilot port and measure pressure directly to the pilot. It should be the same as the inlet pressure minus only 0.2 wci max.
Ok, so spec. is 3.5wci manifold and that's what you're got UNDER FULL HOUSE LOAD, right? Now, work your way through the gas train. Pull each orifice, gauge, and clean as needed. Check the alignment into the venturi and mixer tube. Is each orifice fully engaged into the venturi PMI? Brush out the mixer tube or burners and especially the ports. Inspect them closely. If the venturis are adjustable, check for PMI then adjust as needed. If the ports are clogged or if they have opened up too much can both be a problem. If some ports are clogges while others are more open, you'll get uneven port loading and imbalanced gas distribution to the burners. This can cause whooshing, popping, delayed ignition and extinction popping.
Ok, so you've established everything seems strack all the way to the heat exchanger. Inspect it for obstruction and major breaches. Finding none, what about the collector box, inducer and flue collar? Is there a draft hood or induced? If draft hood, the chimney won't affect combustion since they are not attached to each other. With an induced draft, the chimney will. Now, measure the CAZ WRT the adjoining spaces and outdoors for MUA gradient with the unit firing and air handler running.
If you use a systematic approach ruling out system by system, the problem will reveal itself.
Keep the fire inside the fireplace.
Poor pilot position or incorrect flame pattern matters alot to avoid roll out and snuffing of pilot so don't assume a replaced pilot is correct.
That said, slow or stepped opening valves are what I gather is correct for your app.
I just had a problem like this one. the existing valve was slow opening but went bad somehow. after installing an 8200 series slow opening valve the problem went away. I gathered that the in rush of gas ignited to the point that there was np more oxygen i to sustain combustion.