What's the most economic way to swap rETH(on mainnet) to USCD(on Arbitrum)?

Please let me know if there's a better way to maximize my funds. I only want to be using DEX.

1. Swap rETH (on mainnet) to USDC (on mainnet) on a DEX. Bridge USDC to Arbitrum using Arbitrum bridge at 1:1. (I find I get more USDC for rETH on the mainnet, but bridging USDC will convert it to USDC.e? which isn't good? There's also a swap done on the mainnet which requires more gas.)

2. Bridge rETH from mainnet to Arbitrum on Arbitrum bridge at 1:1. Swap rETH (on Arbitrum) to USDC (on Arbitrum) on a DEX. (I find the rETH to USDC rate is worse on Arbitrum, but you get USDC instead of USDC.e.)

These are the two ways I can think of. Is there a better way? It seems I won't be able to use USDC.e on AAVE, right? Or when you bridge USDC, do you get to select which type of USDC you recieve on Arbitrum? OR is it automatically USDC.e?

Thanks for your input!

ps. Yes, I welcome scammers to message me privately. Please do for mutual entertainment.