The 5.4s are noisy by nature and the totally quiet ones are few in number.
I have a 5.4L (a noisey one) so have been following this since '08 and gathering information from many sources, including here, FoMoCo (off the record) and a nearby Ford dealer. The 10W40 thing doesn't work a lot of the time, or work fully. I.E. it may be a total waste of time, effort and money. A thick-in-grade10W30 HDEO didn't quiet my engine (read on), so I doubt a 10W40 would.
The 5.4L engines are noisy by nature and, for the most part, that noise is benign. Ford knows that well. In the year that 10W40 bulletin came out, they were particularly noisy so they came up with what is more or less a placebo. If you read the bulletin, you will see it is designed to eliminate noise only, not to solve any real mechanical problems. It may or may not relieve the noise but it does create some other issues that make for a sub-optimal operating conditions. The bulletin gave me me pause to think about some of the "group-think" about the 5.4L and I did some experiments.
At the time that bulletin appeared, it had long been said that heavy oils could make the VCT malfunction since it was designed around a 5W20 grade oil. In light of the 10W40 info, I questioned that. As an experiment that started two-plus years ago, I put in 10W30 Motorcraft Super Duty oil, an HDEO designed for use in PSD Fords. I then datalogged the VCT operation on my programmer in a variety of conditions and compared those logs to the ones taken with the engine on 5W20. No difference. That backed up the fact that a heavier oil (at least as heavy as a very thick 10W30) had no effect on VCT operation. That makes sense. If there were issues, it's not likely Ford would allow the use of 10W40, even in a band-aid situation, or recommend 30 grade oils in their overseas markets like Australia.
BUT... I noticed other things like monumentally high oil pressure. My truck has real oil pressure gauges installed (two, on either side of the filter to monitor differential pressure at the filter. The dampened thing on the dash always shows a happy face, so you can't rely on it for much of anything beyond what an idiot lite can do. With 10W30 on cold days, it was not unusual to see 100 PSI oil pressure, even 120 a couple of times (while the dash gage read the same as normal). 10W40 would likely be even higher. I ran 15K on that 10W30 oil, taking UOAs at 5, 10 and 15K( seach the UOA section). The results were fine, but no better than with 5W20, so my limited snapshots of a few UOAs, compared to my previous ones, and all the those on BITOG, showed no wear advantage with a heavier oil. I am now back on 5W20.
Incidentally, the noise issues DID NOT CHANGE WITH THE ADDITION OF 10W30. It was just as noisy as 5W20... or just as quiet, depending on your POV.
I think I provided a smidgen of proof that 10W30, and potentially 10W40, is not particularly harmful to the 5.4L but is it in any way beneficial? IMO, no. The heavier oil increases the likelihood of oil filter bypass and oil pump pressure relief (the valve opens at 70 psi), neither of which is beneficial to the engine. I datalogged the oil filter differential pressure for about 10K miles on my truck with the 10W30 and have done so now that I'm back on 5W20. You can see some of that data in the oil filter section. What I learned is that with the 10W30 oil, filter bypass was most common on cold starts or spirited driving when the oil was below about 160 degrees (which takes 10 miles of steady driving, minimum, in warmish weather). In the same circumstances with 5W20, oil filter bypass virtually never happens, even cold starts at 25F. Less bypass is better than more bypass in the long run.
Thicker oil creates more fluid friction so it will cost you some efficiency... read fuel economy. It's slight and won't show up on a handful of mpg calcs, but it will show up long term with diligent recordkeeping. With 10W30, I didn't see a drop that was outside the margin for error. I can say that after watching it for two years, it did trend downward but, again, not outside the margin for error. 10W40 is considerably thicker. The mpg loss won't hit you hard but it will take some tiny bites.
So, my opinion is that an oil two grades heavier than spec'ed may not be harmful but it isn't beneficial. You need to weigh the importance of reducing or eliminating what is largely a benign noise against the loss of efficiency and the potential impacts on long term wear (as outlined above). Being in Florida gives you a slight climate/temperature edge that will help reduce the downsides, but having seen how the 10W30 operates in hot weather here, IMO the potential for more bypasses and fuel economy losses are still there. If you try it, drive gently during warmups, especially during what passes for "cold" in Florida. It's unlikely you have the means to monitor oil temp as I do but if you drive gently for about 10 miles in 75 deg weather, you will be past 160F OT and are largely safe from filter bypass if you keep the revs below 4000.
I suppose you can try some 10W40 but don't fall victim to the placebo effect as many do here. In my case, it initially seemed like my engine quieted down a little. Wishful thinking on my part. In a couple of weeks, my ear was back in calibration and I realized it was just as noisy. The switch back to 5W20 didn't yield any increased noises. I had steeled myself into total objectivity so was precalibrated to note any changes.