Let's do a back-of-the-envelope calculation. Assume a 5% currency/Nominal GDP ratio. Assume the government/central bank wants to use helicopter money to permanently raise the level of NGDP by 5% above what it would otherwise be. So the stock of currency will be permanently higher by 0.25% of NGDP. And assume currency pays 0% interest, so is not a liability of the government/central bank in any meaningful sense.
So helicopter money finances a deficit of 0.25% of NGDP for one year. It's small beer.
Now suppose the central bank makes NGDP grow at 5% every year (say 2% inflation plus 3% real GDP growth). So helicopter money finances a deficit of 0.25% of NGDP every year. It's small beer, but a continuous flow of small beer. It's normal. This is roughly what happens every year on average in Canada, for example. (But since central bank profits are treated as government revenue in the national accounts, we don't call it a 0.25% "deficit".)
Just a quickie, to get by brain working again, while I gather my strength to disentangle this mare's nest.