As you already listed: "Can the system be demonstrated in a basic undergrad electronics lab?" - so your project must be producible within the capabilities of your labs means. So it must be compatible with the lab equipment you have access to.
I'm a Lab tech at a university and I ALWAYS get students asking for things we don't have or we cannot buy (due to financial, health and saftey, or ethical reasons) or assumed we had them in stock: like obsolete components.
So go to your lab, talk to the technical staff, ask them what they have lying around. Usually inspiration for projects can come from an older project lying around or some odd or unique parts in storage, begging to be used. Also ask them about the equipment they have, if your planning to analyse a 3GHz signal and they only have a spectrum analyser that goes up to 2.4GHz, they're not going to get one just for your project.
Budget: do you have a budget?
sourcing components? does your department have a preferred supplier? Here: we are not allowed to order anything from eBay or non-approved suppliers. Do you have access to a store of components?
I'm confused about the terms of rejection?
Designs that require a single IC, or a simple interconnect of a few ICs.
so it has to have more than one IC with as many interconnects as it can in order for it not to be rejected? cos its going to be pretty hard otherwise to make anything fancy without IC's?