The NVRAM's on ebay et are all relabels or old/used items. The Dallas NVRAMS that have RTD functions haven't been made for so long that even a last production part will be too old now.
But, cutting the top off and replacing the battery is viable with some care (and ideally a mill of some sort), or you can buy a new reproduction if you don't want to make one yourself.
Or just wait a bit for mine to be tested. 
Thanks for the links Terra, duly bookmarked now

The guy on Ebay claims his modules are EXACT functional replacements, yet everything in his ad suggests they don't have an RTC ?!
I guess it does not matter since he is in the USA so I would'nt be able to import it anyway. Plus it would cost me twice what I paid for the scope so... not a good deal at all.
That said, I noticed that my TDS 310 does NOT have an RTC in its NVRAM ! So it's not mandatory for these scopes to run then...
Then I found this page where a guy with a TDS 380, replaced the NVRAM with an FRAM like you suggested to me initially, with NO RTC, yet his scope works just fine he says ! Passes POST, all diagnostics, SPC etc, no visible ill effects. So that's good.
https://www.barbouri.com/2024/06/17/tektronix-tds-380-nvram-replacement/ So I guess the RTC is only used to display the date and time on the screen ?!

However, teh datasheet for the DS1644 says that although you can retrieve the time just by reading the registers, it is not very reliable, you could get corrupted data in case the RTC happens to upfate those registers at the same time you are reading them. So, instead they strongly adise to firsst WRITE a bit in the registers, to stop the RTC from updating the "user" registers, so that no corruption can occur. Then once you have read the time, you WRITE Again that bit to re-enable the register updating.
The time on the screen is updated every second. So that means you have to write the FRAM twice every second 7200 times per hour... what's the endurance of an FRAM ? How many hours of using the scope, would the FRAM survive ? I don't know.
Still, at the least it means we can safely use an SRAM + battery solution instead of an FRAM, like this guy on Ebay sells.
Thanks for the other link on EEVBlog. This time the guy did a proper replacement, SRAM, battery, RTC chip, excellent. Even gives away the Gerber files, how nice of him.
As far as fixing my TDS 340A, the goal is to flip it t make profit, so I must fix the NVRAM issue as cheaply as possible. So no module I guess. I will try to replace the battery and call it a day.
Will try to find tutorials or YT videos on the subject to guide me...
But first I need to practice on my TDS 310 donour to see if I can remove/ desolder the NVRAM without damage. To help without I must first purchase a desoldering gun I guess... I assume wick won't be good or safe enough.
A milling machine ? No such thing but I guess if I buy a Dremel kind of tool and mount it on a stand, drill-press like, like when we used to drill our own PCB's 30 years ago, it might good enough.
Then I also need to get my cheap chinese programmer going, so I can save the original NVRAM just in case, and read/write the replacement should there be a need.
... but the programmers(s USB driver fails to install on my Windows XP virtual machine on Linux, so I am stuck

I also need what gear and S/W is required to clear the error log in these TDS300 scopes, though to be faire I don't understand how there can be any log present if there is no battery left to keep it there once the scope is power off...
And of course I need an appropriate RF gen to calibrate these scopes !
So yeah, lots to do before I can fix my scopes !
So no hurry, you have all the time in the world to polish your prototypes Terra !

Give us a shout on TEA once they are available, to tell us all about them... maybe a video on your YT channel...