between steps 3-5: is copying the tx through these steps a possible compromising vector?
there is no compromising information inside a raw transaction (unless your wallet is broken and does something that is not normally done in a crazy scenario, and since you are apparently talking about an altcoin you might want to double check this) so transferring it will not have any risk.
although if you are doing the transfer using something like USB disk and connecting that disk to the online computer, then it can be infected there and then "infection" can be transferred to the cold storage.
a way to mitigate is is using QR codes for transactions!
if your wallet doesn't support it, then your only option is finding another application on the internet (hopefully an open source one) and generate the QR code using that tool and using a phone you can scan that and do the transfer back and forth.
is the private-key part of steps 1-5 an air-gapped computer vs. the public-key/internet-connected part a node?
yes the private key is kept on the air-gaped offline computer never connecting to the internet.
the public keys are kept on the online computer connected to the internet and the P2P network one way or another.
how do they communicate? QR codes? usb drives?
it can be anything as i explained above. QR codes being the safer option.
I can see how you'd do all that with electrum but there isn't an electrum version for my coin.
usually other wallets offer some sort of command line tool that has additional "expert" lever options. you might have to look into that.
usually these user friendly options are added since there is a demand for it. but if nobody wants it for some altcoin, obviously nobody creates them.
I see the BIP38 encryption thing at bitaddress, but that works only for BTC addr's.
your wallet must offer some sort of encryption (they all do), see if there is an option to encrypt/decrypt private keys using that. if not there are popular tools for encrypting messages (raw data) you can simply use one of them, convert your private key to hexadecimal (base-16) format and encrypt it using one of those tools and AES-256 encryption technique which they must support.