That stiffness should be okay for cutting steel (about 15N/um per your spec), but just remember that the stiffness of the spindle (the bearings, etc), the linear bearings, and leadscrews, nuts and thrust bearings will also contribute to the total machine stiffness. In other words if you only evaluate your stiffness using a simple fea model like you've posted, the final machine stiffness will be lower than what you've calculated. This is not a critique of your method - it's just something I learned while starting to work on my own design.
5in/min sounds really slow. Really, really slow. I know it's a small work envelope, but you might look into increasing that while balancing chip load, available spindle power, and linear thrust and acceleration. There are calculators available on tooling manufacturers' websites that can help with this beyond what I've seen available in Machinery's Handbook, for example: http://mpwr.iscar.com/machiningpwr/ There's also some good info and tutorials available at cnccookbook.com: CNC Milling Feeds and Speeds Cookbook and Tutorial
Some of the cheapest hand tools would also include files and scrapers which can give very high precision, although if you have a time limit associated with a class you might want to stay away from hand scraping anything... But just for example, you could make a precision straight edge from scratch by using the automatic generation of gages principle along with 3 pieces of steel or cast iron, a hand scraper and some spotting fluid. You could also make a square the same way, all of which could be used in aligning your machine and getting flat surfaces to mount linear motion components to (or to be the linear motion components).
What are you thinking about doing for a spindle?