Its your data, your thesis, and your money, and as you noted, you could simply throw money at the problem and duplicate the whole logger enough times that failure is extremely unlikely, but its worth noting that as long as you've got enough storage capacity and processing speed, if the experiment is not convenient to repeat, it is better to log in more detail, including parameters that might be useful but you initially don't expect to need, rather than finding out three months down the line that you need data you haven't logged. Without a sync signal, you cant reconstruct the data set easily/reliably in a multiple fault situation where you've lost different signals from different Arduinos.
It puts me in mind of the astronavigation student I once sailed with who was too lazy to work out his sights immediately after taking them. He had the time, astronomical body, temperature (for refraction corrections), observed altitude, index error etc. all carefully logged and was going on about his intentions to do the sight reduction by computer once back ashore. One small problem: he hadn't logged the E.P, nor did he have the speed and course steered data that would allow him to reconstruct an E.P. day by day by D.R for the sight reduction program or even reduce a simple Sun - run - Sun set of sights, and I don't think he had many if any of multiple star fixes or the occasionally possible Sun Moon fixes that could be reduced directly by spherical trig. After three months of work, finding out from the newbies he was trying to impress that it was all useless and having that confirmed by the skipper didn't help his disposition in the slightest.
I'm not trying to imply you are like that student in any way, I'm just pointing out that if you cant go back for a 'do-over', its gotta be right the first time, and you've got to anticipate *ALL* your future needs.
A mains derived sync signal is *CHEAP*, (especially if you are already using a linear PSU and can get at one end of the secondary before the bridge rectifier), and is remarkably effective.
Another cheap & easy sync signal option would be a lid switch on the weatherproof box I assume you are going to use. That would tag the time each day you open it to swap SD cards.
If you don't care about isolation, the same sync signal can be fed each board via an isolation resistor of a few K. If one board shorts out, as long as there is enough drive from the sync signal source, all the others will still get the signal.
Finally, a GPS module (as suggested by JacquesBBB) can be had for under 20 Euro and would give you an absolute time reference.