I'm really glad that you are listening to feedback.

The same can't be said for many senior users of this forum. When evaluating things like this it is worthwhile to go back to the basics. Does the current setup serve the intended goals of the challenge? Let's think about it. If the main goal is to encourage people to actually run a node and possibly continue to do so after the challenge is over why should we allow low ranked members to join at all? The potential participants are split into several groups:
1) Those who are doing it to learn or want to run a node.
2) Those who are only doing it to earn merit.
The users from group 1 will not care in principle whether they can earn the merit or not. They can participate silently, and if they still want the merit they can join later at a higher rank. This group will not suffer from raising rank requirements.
Furthermore, I want you also to consider why 14 consecutive days? Because the reward is 14 merit? Why should it be that short anyway? Generally I am strongly in favor of having fewer real participants and rewarding them for significant efforts. Why not run the challenge in weeks? It would have several benefits. For the users it would give them more flexibility as they can post their update any day of the week. For the challenge side it would increase the duration of participation that is needed to earn 14 merit and it would reward more consistent and disciplined users.
Anywhere between 8 to 14 weeks would be good. Do you have any personal reasons against it? I can understand that in the current setup it would make it easier to cheat perhaps, but with the expanded setup requiring more information I think that there should be no issues. You must understand that earning 14 merits can be pretty hard unless (we are biased by our perception of users who easily earn this amount of merits, survivorship bias):
1) You join stupid pizza or art contests.
2) You have connections to other users, accounts, local merit farmers.
3) You have good technical knowledge.
Merit comes in waves, (depending on where they are posting) sometimes it can take some users weeks to gain 14 merits if they get it at all all. In addition to this here are my thoughts on your ideas.
2 ) Restrict Jr. Members from joining the challenge
Yes.
3 ) Require a screenshot of the terminal or Bitcoin Core window and disallow text submissions
Maybe, if you don't go with 4 instead.
4 ) Continue to allow text-based submissions but they must be accompanied with a screenshot of the system information neofetch, msinfo32.exe (aka System Information on Windows) or About This Mac
Either 3 or 4 is good, but I think 4 is better. Couldn't in the case of 3 users just trade screenshots? Let's say that I have a node and I just multitask and make screenshots and distribute it among my merit farming buddies or accounts?
5 ) Restrict people who have received more than X% of their total merit in the last 120 days from other/ex participants from joining
Would it be easy to track this in an automated way? If not, don't do it. It seems like it could increase the time needed for evaluating the challenge several times.
6 ) Require a minimum merit amount in the last 120 days to qualify, just like in signature campaigns
Yes.
7 ) Kick out participants who send more than X merit to other/ex participants. Reactionary procedures don't work very well compared to prevention, from my experience.
If you add this as a rule to the contest somehow, could negative trust from defaulttrust be given afterwards? If so, then it would be worthwhile.
8 ) Require getnetworkinfo output in addition to getblockchaininfo, including IP addresses
Good, but not sure about IP addresses because: VPNs and exposing data. I would not want to share the IP of my own node here.
In any case, discontinuing the challenge is not an option at this time. We should not cave in to
Dead Internet Theory and bots/account farms in general.
Good.
But I think system information neofetch/msinfo won't be good, if anyone choose to buy a Rdp/vps server to run these nodes then the system fingerprint might be submited by previously some user's already. Cause those devices are getting used by many user's and handing over to one user's to another user after not renew the deviced.
It is a minor amount of cases. Anyhow, this can be improved by making the screenshots timestamped. Linux users could do
date && uname -a && neofetch and screenshot it. That would give a timestamped screenshot of everything together. There are still ways to fake it but most users will either not have the skills or they won't be willing to take the risk. If the cheating is ever discovered retroactively then you risk your whole account.