I'd be very careful with this.
First, this essentially is teaching yourself instrument flying, and as an instrument instructor, I've found IR training is often extended by the time it takes to unteach the bad habits and procedures people have taught themselves this way -- you're butting heads with the Laws of Primacy and Exercise.
Also, trying to fly IFR with a IFR PIC-legal "safety" pilot in the right seat may be legal, but the record suggests it may not be particularly safe. The average pilot has little or no experience flying "cross-cockpit," and may not be very good at telling when you are starting to "lose the bubble", and no training at all in deciding when it's time to intervene and how to take control from the right seat safely -- i.e., all those things they taught us in instrument instructor training. There have been fatal accidents involving a non-IR PP in the left seat and an instrument-rated PP in the right seat trying to do this.
Go ahead and get flight following to practice talking with ATC and things like that, but don't try to practice IFR procedures you haven't yet learned properly.
What Ron wrote. It is very frustrating, both for the student and the instructor to unteach poor BI. The other side of this is when you talk to a potential CFII about instruction ask how much time they spend on BI. BI is like the fundamentals of a sport. Football players don't love doing hours of tackling and blocking drills. Golfers don't love the hours they spend on a driving range with a golf pro. But if you don't do these things well you won't do them well when you are tired. If the BI is not drilled, drilled and then drilled some more until it is second nature the rest of the instrument flying will be tough. I think every instrument student I have inherited who has had issues finishing up it came back to BI. When I would ask questions about their training they almost always say they started concentrating on approaches day 1, 2 or 3. We would then have to go back to BI and spend several days really learning BI before we could advance again to approaches.
Henning has some good ideas on cross country flying. Get use to busy airspace, talking to ATC, dealing with a towered airport.
In the airplane, learn your systems. If there is an autopilot, learn how to use it. Same with the GPS- learn how to load a flight plan. Learn what every page does in the GPS.
Learn to fly your airplane with precision and know the "numbers". Don't just land the airplane on the runway, land it on a precise spot every time. Be able to fly the approach speeds in your POH. I had one instrument student show up, lesson 1 he landed a Cessna 172, zero flaps 90 knots. We used 8500' and he said that was his normal landing.
We spent the next lesson working on landings.
Be precise in all your flying. If you are using 7500' for your cross country, then fly 7500'. Not 7600', not 7550', 7500'. If the pattern altitude is 1700', then fly it at 1700'. Every time.
By the "numbers", know your pitch/power for different situations. How much pitch for a Vy climb? Vx climb? What is the pitch/power for a 500'/min descent, flaps 10, 85 knots? What is the 90 knot clean cruise power setting? If you understand these concepts VFR it makes it that much easier to teach you BI.