Hey here is my opinion in-terms of schools you posted and to the members I spoke with
1) About Rice it's 100% true what you have written. Current market situation in USA is bad for any visa holders Irrespective of degree and experience considering you will be graduating in Fall 2028 things May be cooling down a bit while you get out of school(God Knows) market might or might not be picking up .... Rice has limited Alumni which is mainly focused in and around Houston(And also concentration mainly on ENERGY AND HEALTHCARE IN HOUSTON) or at the most in Texas. Outside of Texas it will be hard with the degree you earn to earn a good ROI. Also considering the course fee around $130k+ for 2026 Fall Intake I might suggest you can opt for an other B-School of reputed degree(on-paper) which has national recognition instead of localized. So Rice I would keep as a final GO among all the options.
2) ROSS has a higher ranking compared to RICE so I would anytime suggest go for ROSS(EYE'S CLOSED)
3) Mannheim my dream tooo....but if you do not want the visa hurdles in future(as I know the ground reality here) coz I would suggest go with GERMAN option. With the investment you are keeping I would expect the ROI should be 10 times the current investment. So to be on that level at least there should be no visa tensions for nearly 5-8 Years to repay the loan and + savings. Again I do not have idea about current German immigration and PR situation for Indian visa holders and future job perspectives better to talk to students who are pursuing MBA there once.
ORDER IS IF PLANING IN USA: ROSS > RICE
GLOBAL : ROSS>=MANNHEIM >RICE