I dunno if by 1597 there were still all 4 Brunswick lines alive, or if they were down to 3 already, but in any case, all were protestant. The Schmalkaldic League fought some wars there, so by the 1530s things wouldve been easier chanegable, but even so maybe one of them is pragmatic enough to change religion. Of course, in 1597 Germany still operates by the Augsburg Religious Peace, not the Westphalian Treaties, that is "eius regio, cuius religio". If that is enforced that could have major cosnequences in Germany, too - though if its a pragmatic conversion only, the Welf Convert might forego that privilege of his.
Hrm. Looking at Wiki its unbelivable how many protestant bishoprics the Welfs possesse,d either a stitulatory bishops or adjutcators... Now, it seems Henry Julius, ruling Wolfenbüttel, Calenberg and Grubenhagen (so it seems they were indeed down to 2 lines at that time) was a close advisor to the Emperor nontheless. OTOH, and, very conviniently, he is in a succession dispute with the other line, Lüneburg, about Grubenhagen. IOTL, Lüneburg won the dispute before the Imperial Court - of course, only in the next generation, so only Henrys son had to cede the land
But as I undertsand it in 1597 the suit was already on going. So that could be a motivation for him to go to Italy - he gains Modena, Lüneburg gains Grubenhagen. And as said, he seems to have been chummy enough with the Emperor... I dunno if hed convert, but maybe either he does, or the Emperor just hadnwaves that problem away...
I do believe you are right that there were 4 branches; Celle, Dannenberg, Harburg and Wolfenbüttel-Calenberg. I believe that is the order of seniority though I'm not sure of the status of the Harburg branch since its founder abdicated his status of Duke of Brunswick-Lüneburg. Otherwise all members shared that title in common. I've listed all the living male members that I could find. It seems like it would be perfectly acceptable to pass Modena to a second son. As this was done frequently. This would prevent territories in Germany from reverting to Catholicism at first but given the frequency that brother succeeded brother I'm not sure how long it would be before a Duke of Modena and Brunswick inherited physical territory in the HRE.
I kind of like Henry Julius for all the reasons you've mentioned. He seemed moderate vis a vis Catholics though apparently he started a serious witch hunt. He was trained in law and introduced Roman law in place of Saxon law in his domains. He was involved in the arts and architecture building a great deal in the Italian Renaissance style (possibly making Italy attractive). I wonder what his debt situation was like as apparently that caused him trouble eventually (maybe more motivation to convert and grab Modena?).
The Children of Wilhelm Pious/the Younger (1559-1592) constitued the Lüneburg-Celle branch:
Ernest Duke of Brunswick-Lüneburg 1564-1611
Controlled Celle and Hoya
Died without issue leaving Celle to his next brother Christian.
Christian Duke of Brunswick-Lüneburg 1566-1633
Controlled Celle and Hoya 1611-1633
Died without issue leaving Celle to his next brother Augustus.
Augustus Duke of Brunswick-Lüneburg 1568-1636
Controlled Celle and Hoya 1633-1636
Died without issue leaving Celle to his next brother Frederick.
Frederick Duke of Brunswick-Lüneburg 1574-1648
Contolled Celle and Hoya 1636-1648
Died without issue leaving Celle to his nephew Christian Louis (1622-1665)
George Duke of Brunswick-Lüneburg 1582-1641
Controlled Calenberg 1636-1641
Inherited Calenberg after the partition of the Calenberg-Wolfenbüttel territories. Passed Calenberg to his son Christian Louis who in turn passed it to younger brother George William after acceding to Celle. Eventually his decedents consolidate into a single line that forms the Hanover branch.
The Dannenberg Branch:
Henry III, Duke of Brunswick-Lüneburg 1533-1598
Controlled Dannenberg
Julius Ernest, Duke of Brunswick-Lüneburg 1571-1636
Contolled Dannenberg after the death of his father Henry III.
Died without issue passing Dannenberg to his brother Augustus.
Francis 1572-1601
Died without issue.
Augustus, Duke of Brunswick-Lüneburg 1579-1666
Controlled Wolfenbüttel 1644-1666
Inherited Wolfenbüttel in 1635 but could not assume contol until 1644 due to the 30 Years War. Founded the Wolfenbüttel branch that lasted until 1884.
The Harburg Branch:
Otto II, Prince of Harburg 1528-1603
I've also seen him titled Duke of Brunswick-Harburg so he may have had a Ducal title but certainly had no share in the condomium of Lüneburg.
Controlled Harburg as a fief of Lüneburg.
This branch stemed from the morganatic marriage of Otto I (Otto II’s father) so they were not considered Dukes of Brunswick-Lüneburg. The branch died out with Otto II’s son William Augustus 1565-1642.
The Calenberg-Wolfenbüttel Branch:
Henry Julius, Duke of Brunswick-Lüneburg 1564-1613
Controlled: Wolfenbüttel, Calenberg, Göttingen
As you noted they had occupied Grubenhagen but it was disputed with Lüneburg-Celle. His son eventually had to cede it to Christian Louis. It should also be noted that his son Frederick Ulrich died without issue in 1634 after a turbulent reign that saw his territories ravaged during the 30 Years War. This lead to the division of his territories amongst the other branches.