Me thinks no, because of the reason you gave(the gemara reason being careful in how you treat a widow) and in addition she's no longer the status of a widow. Clearly a widow can marry any man(unless kohen, or the son of the previous husband). Clearly once she's re-married you cannot marry her, she's now a married woman! So her status changes from widow to married.
The closest I could come to an authority would be this claim:
The widow's right to maintenance also ceases if she remarries, because under the ketubbah, which is the source of her right, she is entitled to maintenance during widowhood only. According
to most of the authorities, she even loses her maintenance upon her
engagement for a new marriage – although by it alone she does not
create a new personal status – because by it she shows that she no
longer wishes to preserve the honor of her first husband and remain
his widow (Ket. 52b; 54a; Sh. Ar., EH 93:7 and Rema ad loc.).
So once she remarries she no longer has the right to maintenance or other rights provided by the previous marriage. It's logical to follow that an Almanah would no longer be granted the protection/status of a widow as she has given this up.