The majority of whistle players never seek out personal amplification unless they are in an active band situation. Whistles are loud enough that they can be heard un-amplified in most situations except the noisiest.
You've got lots of options. What you do really depends on your immediate needs and future expectations. We should play a game of twenty questions to really get down to what you need but why waste that time. What I usually suggest is that you treat the whistle as though it is a voice. So equipment appropriate for a vocalist might be the most useful. The SM57 is fine, IMO.
I am not familiar with the Tanglewood T6. Might not be a brand available in the US or I have not run across one in my travels anyway. I have played through the Fishman (and its smaller siblings), the Roland (and its bigger brothers) as well as the Bose. The Bose and Fishman are more like PA systems, more on that in a bit.
Yes, an acoustic guitar amp can be appropriate for whistles. The acoustic guitar amp should generally have the full frequency range needed for low to high whistles. There is generally a lo-Z channel for a mic and some built in technology like EQ, feedback suppression and possibly a reverb, chorus and delay (depends on your taste of course). I do use an acoustic guitar amp (Peavey Ecoustic 112) for solo performances largely because it is a self-contained PA system (and it would mostly be me and the guitar anyway, whistles would be an extra). The acoustic guitar amps I like the most of the current crop available over here are the Fishman Loudbox series. The Loudbox Mini is a very nice unit for the money and it is very light and portable. The Roland AC40 is also nice as well. The AC33 is of course a battery powered unit which can be nice if you play out where electricity is not available. Part of the raison d'etre of the Rolands may be lost on whistles though - the stereo chorus effect.
I used an Alesis Nanoverb for some time as the effects unit linked through the effects loop of the Peavey amp. Now I use a TC Helicon Voicelive Touch in front of whatever amplification I use. It has more bells and whistles than most people would require but it really has nice reverbs and delays. One thing that seems to have changed in recent years is that fewer acoustic guitar amps include and effects loop. Designers seem to assume that a pedal board of some sort will be used in front of the guitar amp.
Keyboard amplifiers can also be as useful. They are definitely going to be broad spectrum amps and speakers. Better ones will even offer more channels to afford some additional flexibility in your setup. They may suffer from not having effects loops though since most keys these days have on-board effects.
I prefer the sound of a PA. I have PA systems for venues of different sizes. Smallest ones are monaural. Largest one is stereo. Think about mono versus stereo. A PA system should deliver the best audio quality, IMO. The Fishman and Bose are very good units but they are overkill for most people unless you are making money from your music. Both are top shelf PA systems. I was skeptical of the line array size until I used one (the Fishman first, Bose next). They do a very good job with acoustic instruments. Of course most classic format PA heads and speakers would work as well. A single powered PA speaker with an integral mixer might also be an option. Ad another speaker if/when you need it.
Another option would be to start with a small mixer with some type of powered/amplified speakers. The mixer would give you the connections for mics and instruments. It would surely have an effects/aux send/return loop. Outputs these days might include USB for recording and the usual Main outs for either an amp, PA head or powered speakers. You could use small active monitors for home use at the outset and then move up to larger powered PA speakers when you perform out. Of course you could also plug the mixer right into a home stereo system for starters as well.
The advantages of the mixer/PA system is that it will grow with your needs. Of course an acoustic guitar amp can be plugged into the PA as well. And a mixer could also be plugged into an acoustic guitar amp. So many possibilities.
Your Hall of Fame reverb could be used off any amp/mixer which has an effects out/aux send/return loop. The trick is to match the impedence that the HOF expects since it is designed as a guitar pedal. The HOF reverb presets may be a bit over the top with a whistle - good for guitar and rock vocals though. Don't get me wrong, the HOF has terrific reverbs but they were designed for guitars. I guess if you are good at using the TonePrint software you could get nice reverbs out of it. Most mortals will just use the factory presets though. Since it's what you have there is no reason not to use it in my mind.
Another effects option you might explore down the road would be effects units designed for vocalists. These offer you a couple of things which would work better with a whistle than perhaps the HOF pedal. First they are designed for mic inputs, in other words they have lo-Z XLR inputs and outputs usually. So you run the whistle's mic into the voice effects and then into the amplification system of your choice. Second they should have the effects geared for voice, which can benefit the whistle, like compression - not the guitar sound pump, sustain type but audio leveling type. The array of doublers, reverbs and delays are usually cleaner and less muddy than those usually heard in guitar MEFX units too. You might also get a harmony engine and a looper in there as well. Roland, Digitech and TC Helicon (sister company to TC Electronic, producers of your HOF) are makers with which I am familiar. There are likely others out there.
Those are some of my thoughts for the moment. Hope they are helpful.
I've proven who I am so many times, the magnetic strips worn thin.