I didn't say you can't do it. I also gave the warnings and ways to protect yourself. However, it still is risky. I rip apart old 19" TV's all the time (with a much lighter tube in comparsion to a 27") and they're HEAVY!. If you want to do this you can, but here are the steps you need to do to protect yourself against physical and electrical harm:
1) Buy a 27" arcade monitor frame that can accept your tube out right.
2) Buy a $12 isolation transformer (
www.therealbobroberts.com)
3) Discharge the tube and remove the anode cap and disconnect the neck board and ground wire and remove the electronics from the TV.
4) Remove the 4 corner screws bolting in the tube into the front of the TV plastic frame
5) With help from at least 2 others.. 2 of you lift the tube from the corner flanges while the third person removes the plastic shell from underneath
6) Set the tube on thick carpet or foam.
7) Carefully lower the new 27" arcade frame around the tube.

Run the bolts (that came with the frame) thru the flanges from underneath and use washers and nylon lock nuts on the back
9) Ensure frame is secure, then figue out a way to mount the electronics board to the monitor frame base. Use nylon/plastic stand offs to isolate from metal frame.
10) Reattach ground wire and anode cap and degauss wires and neck board.
11) Cut the power cord close to the monitor leaving at least 12" of cord.
12) Mount the isolation transformer to the monitor frame, isolating it with nylon or something
13) Attach the cut cord still attached to the monitor to the hot and neutral OUTPUT side of the isolation transformer (white line = neutral, black = hot)
14) Attached the bare cord cut to the INPUT side of the isolation transformer
15) Plug in the TV and see if it works. (NOTHING connected yet)
16) Take a voltometer (digital multimeter) set on 200V AC and touch one lead to the frame of the monitor and another to the grounding screw in an outlet plate. Should show 0 volts. If it's hot, then you didn't wire the isolation transformer correctly.
The rest is up to you. I would NOT suggest cutting a board to surround the monitor and mounting it to the monitor frame (a 27" tube may be too much for the boards, unless perhaps you used 2. 3/4" boards sandwiched together). Instead mount the frame to board and use a thin board around the front of the monitor to surround it instead (for looks, but NOT for support).
I'd use sturdy support (like vertical running 2x4's or at least sheets of 3/4" running against the inside of the case) to support the monitor shelf. Don't just support the shelf with 1x1's screwed into the sides.. They will break and your monitor will fall. Also you can use metal bracing too (but more expensive, harder to cut)
Before you discharge the tube learn about discharging and safety issues. Before you remove the neck board, understand the parts associated with the monitor, and the risk of breaking the tube messing around at it's weakest point (the back of the neck where it's the thinnest).
Like I said, it can be done, but you need to know the risks, both physically (weight, glass, structurally) and electrically before your start this.