Multiple Tracking Codes - What do you do?

They may be concerned about slowing page loading time, which does affect SERPs. Perhaps they can test this on a test server?

They can use async jquery to help. They can also put the code at the bottom to execute last. I don't know of other ways to fix this though.

Without munchkin, you will be unable to do form prefill and to monitor lead behavior on the site, thus reducing the information available to Sales.

You can also ask to track certain pages  as a compromise - pick the sections you must have.

As Josh said, the way the tracking codes would negatively impact SEO is if they slow down page load time, which the munchkin is not known for doing.  There are MANY other things that impact page load time aside from a couple tracking scripts.  Have them put the codes at the bottom of the page 

And look into a tag management solution so you can change the codes moving forward without requesting IT support.  Google offers a free one: http://analytics.blogspot.com/2012/10/google-tag-manager.html.

+1 for Google Tag Manager. We use GA, Optimizely, Marketo, and all other kinds of software that require scripts on certain pages, and Google Tag Manager makes it way easier to control which scripts are thrown on each page.