Bottom line: I've scoured the record transcriptions at the Polish website BaSIA for any new entries on my Gramlewicz question and found nothing.
After a rollicking start like that, the question is: now what? The answer: I'm not sure.
Sometimes, when you need to sort through records, the best approach is not to be afraid to get your hands muddy with the mess. Don't run away from it. Look deeper to see if there are any patterns. Somewhere in the murky midst, you might find a clue.
The only clue I've found this go-round was that there may have been more Gramlewicz families in tiny Żerków than I had at first suspected. This may get messier than expected.
While wandering around, though, I realized a few things. First is that date gaps in record collections may mean the very records I'm seeking are somewhere in that gap. Don't give up the hope of finding something until the entire record set is available to use.
My second realization is that thinking phonetically is still an important research skill. Remember that there is more than one line of Gramlewicz-Laskowski marriages on my "most wanted" list. A funny thing happened on the website when, instead of searching only for Gramlewicz, I tried putting the website through its paces with the surname Laskowski: the search engine couldn't come up with a single Laskowski result for me in Żerków. I tried a different approach: do the same thing as happened to another line of Laskowskis when they immigrated to New York. I pronounced the surname like a Polish person might, then thought how an English-speaking listener might spell what he heard. Searching for Laskoski (from a misunderstood "Laskovski") instead of Laskowski suddenly produced results. I'll need to remember that for future searches.
My third thought was to make a note of all the other Gramlewicz family discoveries I saw on the BaSIA website, even though I can't fit them into my tree right now. Those search results might come in handy in the future, and having a catalog of those other Gramlewicz lines in Żerków will make it easier to plug them into my tree if and when I figure out the connection.
Bonus realization: there is a way to access the scanned documents from which the transcriptions were extracted. While the scans seem unresponsive to manipulation on my computer, at least I can try to read them for myself now.
While I'm grinding through that records search project in the background, though, there is one piece of unfinished business I can attend to now. It's time to revisit that Polish DNA match at MyHeritage and document the connection from the current generation back to the time of Elżbieta Gramlewicz's likely sister Katarzyna.