(Re-edited for the sake of clarity.)

I solved my problem in an unorthodox way, as you will see.

First I tried the Unix mailboxes method. I created a temporary Unix mailbox in Pegasus Mail, copied a mail folder's messages into it and imported the mailbox into The Bat!. Success! Then I deleted the previous messages fr om the Unix mailbox and proceeded to do the same with another mail folder. Surprise: the messages fr om that first processed folder reappeared along with the new ones.

I had never used Unix mailboxes before, and didn't know that they have reduced functionality in Pegasus Mail, compared to its native-format mailboxes. One of the missing functions is "Recover deleted space" (equivalent to "Compact folder") - you just can't compact a Unix mailbox in Pegasus Mail. So, it just keeps growing indefinitely, as apparently Pegasus only marks deleted messages as such, but doesn't really remove them. And unfortunately, The Bat! doesn't recognise the deletion marks and imports the "deleted" messages all over again.

It would be useless to apply The Bat!'s de-duping function, because I would have distributed the duplicate messages to different folders. Even if I kept all messages temporarily in the same folder, it would be impracticable to sort more than 48,000 messages into over 120 folders before I learned to use The Bat!'s filters, which I hadn't yet. And even the filters wouldn't be able to sort *all* messages, for subjective criteria often apply.

Then I tried deleting the Unix mailbox and creating a new one for each folder I wanted to process, so that it contained only fresh messages to be imported. It was obviously an extremely laborious and tedious task, but it was working - until I reached a certain folder where there were messages missing and some others corrupted. I gave up: definitely, Unix mailboxes are not a feasible or reliable method, unless one has only one or just a few simple mailboxes (not my case) and checks the results.

There were two further options left: either I tried some conversion program that exported Pegasus' mailboxes to a format that The Bat! could read, or I tried the IMAP solution. I didn't want to use IMAP, because that would entail a lot of hassle configuring everything, duplicating the large and complex folder structure, etc. So I started to search for a conversion utility.

I found two categories of them: the first was very old utilities (most without any new version since the 1990s, and often DOS-based!) that would probably not properly convert messages with more modern formats and features (MIME, HTML especially with inline objects, etc.). Most of them were also very specific and exported Pegasus' mailboxes to some other proprietary format, usually long-gone.

The second category was paid (and expensive) utilities that would do what I wanted, but at a steep price.

But convenience had the final word, and I used one of those paid utilities. I won't tell you which, because I used a cracked copy... I'm not proud of what I did, but I can't say that I'm terribly ashamed either, because no way I would pay a hefty price for a one-time-only operation, intended just to try another program. And they didn't have free trial versions. But I must say that if I had some permanent use for "software X", I would gladly pay for it: the program in question is excellent and did its job flawlessly, converting each Pegasus mailbox into a Windows folder (with subfolders appropriately nested), and each message into an EML file inside the Windows folder corresponding to the original Pegasus mailbox it belonged to. It was done quickly, easily and without a glitch.

From then on, The Bat! imported the EML files perfectly, and although it was a tedious task to perform one import for each mail folder, otherwise all went well.

Now I'm running The Bat! and Pegasus in parallel; I configured all my e-mail accounts in The Bat! to leave messages on the servers after download, then I download the messages again with Pegasus, letting it process them normally and delete them from the servers. This will allow me to find how to do the things I'm used to doing in Pegasus, if possible. I'm trying to use mostly The Bat! for replies and new messages, but I must say that it is the first program I try that will force me to use the entire 30-day trial period. Pegasus is powerful but not necessarily difficult or obscure, and it is extremely well documented (it had to be, because for a long time David Harris financed it by selling manuals, and he did a very good job - as with everything he did). So far, I can't say the same about The Bat!, whose documentation is nothing short of mediocre. Sorry, guys, but even at version 4.2.9 this is a sad truth.

Mission accomplished, but one thing still puzzles me: I noticed that all of the few Pegasus mailboxes that The Bat! successfully imported directly were among my oldest ones, created more than a decade ago, when I first started using Pegasus, then maybe at version 2.2 or so. As far as I know, Pegasus Mail's PMI and PMM formats have not been changed since then (when you create a new mailbox in Pegasus Mail's current version 4.51, it still offers the choice of Unix or "Pegasus Mail 2.x" format); over the years, as I migrated to successively newer Pegasus versions, they wrote and changed those mailboxes as well. Anyway, setting aside that mystery, I would guess that Ritlabs worked with a very old version of Pegasus when The Bat! was still suckling and learning to fly, and never worked with it again...

Anyway, thanks to Marck and Arnold for the tips, and here is my experience recorded for posterity...