I have a project licensed under the EUPLv1.2 license, and I want to incorporate GPLv3-licensed code in it. However, due to the GPL's copyleft, that is not legally possible.
It is not legally possible to distribute the resulting derived work under the EUPLv1.2 license, because the GPLv3 license does not allow that.
However, it is possible to distribute the resulting derived work under the GPLv3 license.
If you are the (sole) copyright owner of the EUPL work, then you always have the possibility to change the license, but even if you are not the copyright owner, the EUPL allows you to change the license to an enumerated set of other licenses and the GPL happens to be on that list.
Is it possible to dual-license the project with both licenses (EUPLv1.2 and GPLv3) to allow for the GPLv3-licensed code to be incorporated in it, despite incompatibility with EUPLv1.2?
No. Dual licensing gives the recipients of your code a choice which license terms they want to follow, but it does not help you to get around license incompatibilities.
Technically, you could dual-license the project (assuming you are the copyright holder of the EUPL code), but effectively your users would only be able to choose to follow the GPL license due to the dependency on the GPL code.