Talked to Namecheap support. They said it wouldn't be possible for me to transfer funds into that account. While I can pay bills for the current domain, I can't add money to the account.
I've looked at my usual registrar, name.com, and they have subaccounts which can be used to let another person have full control of the domain. It would probably be $2 more a year, but if it's more convenient, it's probably worth it.
I was waiting until we got to 60 days so we got a full extra year of renewal when I transfer the domain. And...
perl6 -e 'DateTime.new("2018-05-07T11:57:08Z").later( :60days ).say'
Hey, great timing John! @revi can you send me a request this time for a transfer? I'll take care of it right away.
> whois miraheze.com Domain Name: MIRAHEZE.COM Registry Domain ID: 2122689320_DOMAIN_COM-VRSN Registrar WHOIS Server: whois.name.com Registrar URL: http://www.name.com Updated Date: 2018-08-02T04:31:02Z
Looks like status is Resolved.