Basically, how big of a payment you can do depends on how much volume there is. It's a positive feedback loop, though.

There will be a distribution of transaction values with a median less than the mean, as seen in credit cards, swift, and all other payment systems. There's a long tail of large value transactions that would have to wait longer. So if you buy a car you'd have to wait for the equivalent of 1000 more car-valued transactions to occur, but this is helped by the ton of smaller-valued transactions backing you up.

If the maximum someone is willing to wait for a transaction to be confirmed is 1 hour, then the ceiling of acceptable transaction value is 0.1% of the sum of total value transacted per hour, but this gradually rises as the system gets more popular. If you think about it, a similar phenomenon happens in any payment scheme, more or less. Even Bitcoin would make you wait a long time for a trillion dollar transaction because the cost of mining a double-spend would take a long time to reach a trillion dollars. In the early days you wouldn't trust it with even a $10,000 transaction because anyone could farm out a huge mining operation.

I had some funding, worked on it for a year solid, built working prototypes, learned a lot, prepared for a whitepaper, but then I realized that an attacker could still profitably double-spend if they made a ton of small payments at the same block to different people. This would show up as a suspiciously-large transaction volume though...

I think it means that (worst case) to accept an avg payment you'd have to wait for 1000 avg blocks instead of 1000 avg transactions...? If the fee was 1%, instead, though, you'd only have to wait 100 blocks, so it becomes reasonable? I'm kind of stuck and have nobody to talk to about it...

Edit: You've inspired me to again work on this! Thanks!

Let's consider this "worst-case" scenario with 100% of txs are made by the same attacker with an intent to double-spend. Before generalizing, let's fix the amounts to 1000 txs/block with a payment price of $100/tx with a $1 fee/tx.

Block 1: The attacker sends 1000 txs (the "payments") worth $100 each to 1000 different merchants. He pays $1000 in fees. He stands to have revenues of 1000 x $100 = $100,000 if he can double-spend the payments. His payments are currently buried by 1000 x $1 = $1000 in their own fee costs, for a net profit of $99,000 if the merchants accept his payments right now. The merchants are cynical and rationally choose to wait until this block is buried by 1000 x 100 x $1 fee/tx = $100,000 in fees before accepting the payments. (It doesn't even matter if they know he's trying to double-spend or not).

Block 2: The attacker sends 1000 loopback txs to himself to bury his payments in another 1000 x $1 = $1000 of fees. $98,000 to go...

Block 3, 4, 5, ... 100: The attacker sends 1000 loopback txs to himself per block for 98 blocks to bury his payments in another 1000 x $1 x 98 = $98,000 of fees for a total of $100,000 in costs. The merchants are now satisfied with the payments and accept them as honest transactions. The merchants send the attacker $100,000 in goods.

At this point, the attacker replaces block 1 with another block that is just full of loopback txs to himself rather than payments to the merchant. He then replaces blocks 2-100 with a new set filled with loopbacks. Then he makes block 101 with one loopback tx to himself so as to outbury the old blockchain with an extra $1.

The attacker's current revenues are $100,000 in goods, but he had to pay $100,001 in fees to do it.

We can generalize this to mean that to trust a transaction, worst-case, you have to wait until the the total payment value of the block itself is buried by its own value in transaction fees. Therefore, you'd have to enforce minimum % fees because, if you allow low transaction fees then an attacker could send a huge loopback transaction that makes everyone else in the block to have to wait a long, long time until enough fees bury that block. Maybe you could solve this using fixed block sizes that force transactions to have to bid for a spot. I guess you have to do that anyway, though...