The idea I have is that users will be from a wide variety of economic situations, and mandating a minimum excludes those with less resources, who still have need of the system and the option to run relays.

At the top of this page you can see that there are transactions all the way down to 1 satoshi. So using such a fee, and the fact it doesn't have to clear before a few days, one can cycle two amounts to keep one constantly in the air and satisfy the requirement.

So an amount that is reasonable for a poor person, kept continuously locked up, serves as a proof of age of the relay, while their routing fees will likely earn them more than enough to increase this amount in order to improve the number of new clients they get.

Of course, one has to open channels to run an Indranet relay, which is a mandatory up front cost. A sybil attacker will not want to open up long living channels, so the amount of time a HTLC is locked in the channel also can be a data point to select a relay for first time use. Keep in mind also that the cost/time delay for closing them can be quite high so this also raises the bar for a profitable scam.

But HTLCs can be closed at any time, where a timelocked transaction cannot be spent until the specified block height is passed.

The other thing that the time locked transaction used in association with a relay's identity is objective proof of the time the node has been running, which will constitute the largest factor in the amount of new clients a node can attract. Sybil attackers window of opportunity is quite small, really, especially if their relay doesn't get a lot of use in the beginning. So, proof of the time of setup and the age of the node is definitely the most effective defense against attempts to capture fees without delivering service.

A final point - the amount of service purchased at a time can be very very small. The client just needs a few megabytes ahead of current usage and new payments can be streamed fee-free. This could be in the range of 5-50 sat renewed every few minutes.

I think with these measures in place there would be very little risk of sybil attacks since there just won't be the economic incentive