"But as per them, converted money is accounted separately"
Nothing in the tax code provides for such separate accounting. You, not the custodian, are the one responsible for maintaining the accounting of your contribution and conversion basis, particularly because you could have many Roth IRAs and could transfer funds between them. Money in an IRA account is fungible, it's not treated as having come from any particular source.
I calculating the attributable gain or loss on the $1,500 excess contribution, when determining the adjusted opening balance the $4,500 deposited into the Roth IRA as a conversion gets added to the balance that the Roth IRA had immediately following the excess $1,500 contribution. When determining the adjusted closing balance the $1,500 distributed as a regular distribution gets added to the balance in the account immediately prior to the recharacterization or return of contribution. https://www.law.cornell.edu/cfr/text/26/1.408-11
If you do get them to perform a recharacterization or return of the the $1,500 excess contribution, your earlier $1,500 distribution would still be an early distribution that is too late to roll over. However, because all of the other funding of your Roth IRA(s) came from nontaxable conversions, this distribution would be from your nontaxable conversion basis and would therefore not be subject to the 10% early-distribution penalty that would otherwise apply.
