Cost is not the issue, Each Block has a defined target of say 1 minute between blocks.
Your chain is 3 months behind, and still has a target time of 1 minute, your block height will always be ~ the same 3 months behind and as such never a threat to causing a reorg, because a reorg can only happen if your block height # exceeds the main chain.
So how do you make up the 3 months time difference?
FYI:
Any change to the code to modify the time target between blocks could allow faster blocks, would lower the target difficulty making it a weaker chain and also break consensus with the other nodes, therefore making sure it would never be accepted over the main chain.
FYI2:
The phrase (block production has zero cost) , is incorrect.
There actually is a cost , it is time.
Your block has to wait the coded time before block generation can occur, and those coins go dormant for a coded period, another time factor.
The Time between blocks is hard coded which affects the difficulty # in proof of stake coins, thus defining the strength or weakness of a chain.
I really hope you're not the developer of that coin in your sig, because you seem to have some fundamental misconceptions about consensus design.
1) I have already said this above, but I'm going to restate it in plain terms: any concept of time elapsed in a trustless system is utterly unverifiable without an objective measure such as PoW, which is an unforgable proxy for elapsed time
2) In PoS block production has zero cost, see 1)