I could be wrong, but I think the problem is you are doing incorrect data type conversion.
You are dividing an int by an int which will produce an int....

No problem.  As for IT being repetitive, it depends on where you work as well.  Where I work, I was slowly building up a list of canned responses to people...

The best approach (from my understanding) is to not force reuse of old values.  The primary key, for best performance, should be an ever increasing value.

Why do you...

So 1/6 of your data has the longest MethodNames.  This is likely part of what is causing the slowness.
What is the max length of that column?

Also, what...

We have things set up that way where I work.

The only thing you need to be careful of is that SSIS operates in separate memory space than SQL...

It is free and works for most things.  Anybody who has worked with a 2012 SSIS catalog (possibly 2014 and 2016 as well... I did not test those) has probably...

Not to be mean, but if you can't adjust the query and you can't de-duplicate the data, what do the developers think you can do?

The only other option...

Looking at the execution plan, the slowness appears to be caused by the sorting which is due to the DISTINCT.

It looks like you have a LOT of duplicate...

1 - My education is some university, no degree.  Plus I got my MTA in database fundamentals.  Experience is 7 years as a database administrator and current position database administrator

Ok, if you need to sum those up, you would want something more like:
SELECT TOP 1 passenger_name, fare + commission + gst AS total_cost
FROM ##invoice
WHERE...