How to get IATS working
If with EOL you mean End Of Life - you are mistaken! iATS 1.5.3 is already working for many transaction pathways in 4.7.x - but we will not release an official release until ALL 21 type of transactions, payment processor switches, chq debit img swapping, encrypted swipe is working as it currently is on 4.6.x LTS. 

In general before upgrading any site you will really want to check to ensure that ALL extensions that you have enabled have releases for the CiviCRM version you're upgrading to - otherwise you're taking a risk. 

A number of sites [from at least 3 CiviCRM partners that I know of and likely more] are already transacting with iATS on 4.7.x - they would have created a staging copy to check that their pathways are working. 

So I'm not sure what issues you're running into. Are you using TLS 1.2? Is SOAP enabled? Any clues in the iats log tables? agent code/password correct - and configured properly? 

See iATS Extension - README.md file:
9002 Error - if you get this when trying to make a contribution, then you're getting that error back from the iATS server due to an account misconfiguration. One source is due to some special characters in your passwd.

Also: Please have a look at the link http://home.iatspayments.com/Relaunch-SHA256 and check if your environment is compatible.

EDIT: to test if your server environment is indeed TLS 1.2 - go into your CiviCRM -> Payment Processor configuration and edit the URLs from www to www2 - so: e.g.:
https://www2.iatspayments.com/NetGate/ProcessLinkv2.asmx?WSDL
Run a transaction - if this works [if this does not produce a 9002 error] - then your server environment is -not- TLS 1.2