The explanation of why they can't match is fairly straight forward. If the original subject contains colours that can exist within ProPhoto RGB (or Adobe RGB) but not in sRGB, then the web-ready image can't match the wider gamut versions of the image. As a very simplistic analogy, it's like having a 5 gallon, 10 gallon and 20 gallon bucket. If you have 12 gallons of water to carry and need to do it in one load, then clearly you need the 20 gallon bucket even though it's overkill. A 10 gallon bucket falls a bit short, while the 5 gallon bucket falls very short. Of course if you only have 4.5 gallons to carry, then any of them will work.
Conversion between colour spaces will only produce perceptually "the same" results if the source colours all fall within the colour gamut of all of the colour spaces involved. The fact is your camera can capture colours that lie outside the gamut of sRGB. You haven't said what monitor you're using for your digital workflow, but it's likely that it can reproduce beyond-sRGB colours as well. You said in the original post "if I convert the original prophoto image to an untagged format, they are comparable". Well, "untagged" likely means the unprocessed RGB colour data is being dumped straight to your system's video pipeline. If it looks comparable to the ProPhoto RGB version of the file in Photoshop, this means you're probably running a wide gamut display that naturally reproduces colour well beyond the range of sRGB.
You haven't said what kind of print is ultimately being targeted for the repro files. But if it's inkjet print, then the printer, ink and media also certainly will be able to reproduce colours that are beyond what sRGB can represent. Basically, sRGB is a 5 gallon bucket and everything else you're dealing with involves more than 5 gallons.
We do some artwork repro where I work, and our workflow is similar to what you've described. We shoot the originals with Phase medium format gear, polarized strobes, colour checker charts for white balancing, etc. and develop in a 16-bit ProPhoto RGB workflow viewed on NEC wide gamut displays. For original artworks involving lots of saturated colours (certain textiles, acrylic paints, etc.) we'd absolutely expect than an sRGB-converted version of the repro file would never look like the original artwork, nor like our master digital repro file.
If you have a client that's hyper concerned about colour matching, and the original work contains highly saturated colours, then most likely you simply won't be able to do it via sRGB images over the web. If you can't compare the on-screen wide gamut version of the file, nor the printed repro, directly to the original, then yes it will be a guessing game.
Note that, setting aside the web / sRGB issue (which is kind of a sideline issue in the art repro scenario), it's quite possible that you won't be able to reproduce some of artwork original colours accurately anyway. They may simply lie outside the gamut of what your combined, end-to-end colour system can achieve. Colour spaces overlap each other in irregular ways. Some colours from the original artwork may lie inside the gamut of some parts of your workflow, but outside the gamut of other parts. The maximum colour that you'll be able to reproduce with some level of accuracy will be the lowest common denominator of your entire end-to-end system. The two normal limiting factors are the original in-camera RAW capture, and the final print. In between you can work with higher fidelity if you so choose, but it won't necessarily help you if the camera couldn't capture the colour in the first place, or the printer can't print it.
