First of all, what you plan does not satisfy the OSI definition of Open Source. Some people are quite touchy about that, so I recommend not using the label Open Source anywhere.
Unfortunately I don't know any accepted term for licenses that make the source code available but are too restrictive to be considered Open Source. Microsoft calls this their Shared Source program, but I haven't seen that term in other contexts.
I wouldn't start with a permissive license like MIT, since the spirit of what you want to achieve is pretty far from MIT.
The Microsoft Reference Source License looks pretty similar to what you want.
The relevant clauses are:
"Reference use" means use of the software within your company as a reference, in read only form, for the sole purposes of debugging your products, maintaining your products, or enhancing the interoperability of your products with the software, and specifically excludes the right to distribute the software outside of your company.
Copyright Grant- Subject to the terms of this license, the Licensor grants you a non-transferable, non-exclusive, worldwide, royalty-free copyright license to reproduce the software for reference use.
I'm not sure if the license itself is protected by copyright, so you might not be able to simply use it.