What's a bit confusing for us ... and for you as well is that the ActiveState Software company, as you point out, also owns registrations -- we counted at least four -- for other Perl-related trademarks. Possibly the foundation and ActiveState -- which makes and sells commercial proprietary Perl software -- have reached an agreement as to their mutual use, possibly based on ActiveStates' prior registrations. That's just a guess and hopefully a reader will provide more details for a follow-up response. By the way, ActiveState also applied for VISUAL PERL as a trademark but that application was rejected for the Principal Register (as being descriptive) and was relegated to the less-than-cool Supplemental Register. In any case, there are two entities claiming federal trademark rights for PERL and that does not bode well for your intended use.
Let's not forget about the camel ... There's also a third Perl trademark in action and that's the camel associated with O'Reilly Perl books. (O'Reilly also owns the "perl.com" domain.). Perhaps that has something to do with the fact that Larry Walls, the creator of Perl, works for O'Reilly, and is the author of their guide to Perl, nicknamed the Camel Book.
Hurdles and More Hurdles. The Dear Rich Staff believes that you have a series of challenges ahead of you -- for example, a trademark examiner may object to your use based upon the existing registrations; or ActiveState and the Perl Foundation may oppose the registrations as being likely to confuse. For these reasons, we'd probably back off the choice of AlchemicPerl. In addition, you might be concerned about the use of the prefix, "ALCHEMIC" and "ALCHEMY." We just got a solicitation in the mail from an Alchemy Software company in Texas, and we see a company in Florida is seeking a federal registration for ALCHEMY (which might be a problem considering there already is an existing registration for ALCHEMY for computer software for data and document capture.) And there's also a web production company called Alchemic Productions.