AJH,
I can't address the Bradshaw unit since I'm not familiar with it. However, the Keeley Compressor, while pretty much the standard in boutique compressors, won't do much to tighten up your Triple Rec. In order to understand this, we must first get a little more clear in defining what "tightening up" a Recto really means, since it's not exactly put together with loose-fitting nuts and bolts.
Firstly, it means reducing some of the ~200Hz content of the frequency response. This is because these frequencies more than any others are responsible for that sound we commonly refer to as mud. The result of too much of this frequency range in your sound is that, no matter much you turn up the bass, it will not get 'chunkier' and more percussive sounding, it will simply be louder and louder mud.
The next aspect of 'tightening' is to (optionally) add in just a little ~100Hz bass to make up for the cut you made in the bass at~200Hz. These lower frequencies aren't necessarily more musical, and can cause just as many problems in a studio recording situation as the 200's, but they do impart a more percussive quality (think: thump & chug) to the live sound of a guitar amp, especially in a head/cab rig.
The third aspect of 'tightening', which applies especially well to the Recto series of amps, is to reintroduce some missing mid-range frequencies back to the signal. Marshall Plexi's and JCM-800's of the 1970's and 80's were famous for providing a truly 'singing' guitar tone, especially in solos, and perhaps most notably when famously paired with a Gibson Les Paul. Let's face it, Marshall is famous for defining 90% of what rock n' roll guitar is.
When Randall created a successful alternative to that sound with the Recto series, he had to accomplish a few things to make it a true alternative, and not just another also-ran, to the hotrodded Marshall sound that ruled at the time. He had to provide more bass response than the Marshalls did. This was because this was unapologetically a heavy metal guitar amp, regardless of whatever else you can do with it. Part of this was accomplished by using 6L6's for power tubes instead of the less-bassy EL-34's that Marshalls used. Another part was by tuning the Recto's tone stack to give more lower mids instead of the medium-to-high mids that Marshall was famous for. This gave the amp a darker sound with fuller bass. Unfortunately, it left it more vulnerable than the Marshall for the bass to get muddy in the process.
He also had to provide more scooped and compressed mids right off the bat, since it had become quite fashionable to use EQ's of various kinds to scoop the mids, especially at 800Hz, out of the classically mid-heavy Marshalls in order to approximate the sound that Metallica and other thrash metal bands had established as the heavier-than-thou sound of the time.
The result was one of the heaviest guitar amps ever made. Without the aid of effects or EQ's, the stock Recto crushed the stock JCM-800 for heavy metal rhythm guitar and for pure gain, and thus began the conversion of many younger guitarists away from Marshall's lock on the heavy metal market and over to Mesa.
However, one of the prices paid for that triumph was the frank loss of some of the mid-range frequency response so essential to good solo tone, and while Mesa made an amp that crushed the Marshall for heavy rhythm tone, it did so by sacrificing the solo tone noticeably. At the time, this was a smart gamble on Randall's part, since the trend in music was not only toward heavier rhythm, but also completely away from what was seen at the time as the solo excess of the 80's. With hindsight, it's now generally accepted that the pendulum swung too far in the other direction, and the result was that the 90's were perhaps the lowest period for electric guitar solos since before Chuck Berry popularized its use.
Frankly, Randall could afford not to care too much what his changes did to the solo tone of his new revolutionary amp, because the users themselves didn't care about their own solo tone in the slightest. They just wanted heavier, lower and louder...and they got it.
What the Maxon OD808 and other types of overdrive can do is to give a much-needed boost to the mids and upper mids (~600Hz to ~3.2kHz) that not only helps your solo tone to get back the "singing" quality that's been generally missing for the last 15 years in solos since the Recto took over as the most recorded amp, it also brings some life back to your power chords and single-note riffs by helping them cut through the mix more.
BTW, the Maxon OD808 is a fine overdrive pedal for that purpose. If you like Keeley's products, you should hear what he does with a Boss SD-1. I've got one of his 5-Star modded ones and it's absolutely incredible as an overdrive. The Katana is not an overdrive, per se, it is a clean boost, and a very good one. It does, however, have an optional switch that adds some very nice harmonic content to its boosting capability. Keeley's Java Boost is also not an overdrive, in the classic sense, nor is it a clean boost either. That doesn't stop me from recommending it (or equivalent products) as perhaps the single best thing you can do for your solo tone if you're a Triple Rec user, which I am.
Treble boosters like the Java Boost have two main effects on your guitar sound. First, they act as a preamp for the treble frequencies, meaning the higher the frequency, the more it gets boosted. This allows incredible amounts of gain on the higher notes of your solos, with all the extra sustain that comes with it, without simultaneously muddying up your bass, something that is difficult to impossible to do with overdrives.
The other main effect comes from the fact that they use real germanium transistors, which have the peculiar and wonderful attribute of adding in lots of even-order harmonics to your sound when overdriven. Nothing else on the market helps your guitar's solo tone "sing" through a tube amp the way a good boutique-level germanium treble booster can.
Mostly because I can make a product of at least equal quality for much less than some of the bigger name guys charge, and I give a lifetime warranty on materials and workmanship on everything I sell.
