AMIE course is only recognized if you have enrolled before 31st May 2013. After that date, if anyone has enrolled, there is no recognition at present. The matter is in Delhi High Court since 7 years. So you can rule out the AMIE option.
BITS WILP is not a very good idea either. Supreme Court in it’s 2017 judgement clearly said that engineering education must involve face to face teaching inside four walls. The present rules are too strict to allow online education for engineering in India. Things are changing a bit with covid pandemic now but clear recognition must exist before you enrol for a course, otherwise it’s a total waste of your time and money.
There are many part time M.Tech options but finding a part time B.Tech option along with job will be very tough in India.
So if you can quit your job and get a lateral entry in 2nd year of regular BE in a recognized course/college/university, that might be the only way forward for you. Try to look for NBA accredited BE courses as they have more global acceptance under Washington Accor