Hex beam is a great antenna however it does not meet your omnidirectional requirements. The cobweb antenna will meet your requirements.
I would suggest the CobWeb Antenna, mounted at a decent height it will outperform you vertical if mounted high enough. It looks neater than a hexbeam. I use one for portable operation from my camper van and it works great. When I have done shootouts with other friends of mine, using the cobweb and comparing it too good verticals and things like the spiderbeams, the cobweb was very close to being equal. Most stations could not tell the difference between me using the cobweb at 40ft and my friend who uses a hexbeam. The station we used for the test had a calibrated S-meter and is a friend who was being honest. This means little because its a DX path with huge fading. Its just an anecdotal test to confirm that the cobweb at least works. Other stations reported difference which were ridiculous because most were using useless guess meters typically found on transceivers.
I suggest using this simple version of the cobweb antenna.
http://www.karinya.net/g3txq/cobweb/There are many homebrew articles on the web for the cobweb. You can also buy a commercial version from the UK.
Good luck with keeping the XYL happy, I had to divorce my XXYL because she did not like my towers. She knew I had my towers and ham radio when I met her, and I was unwilling to compromise. I have good
XYL now who seems to like the look of my towers and ham radio. She actually likes listening to CW when she is cooking she says its relaxing like music. I was shocked but happy!
Have a vertical ground mounted since I have very little yard and also want to keep the wife happy as it is a new house. I am thinking of putting up a hex beam approximately 30 ft high on one end of the house and eliminating the vertical. The vertical is in such a position that should everything happen in the right (or wrong) sequence of events it could possibly end up in a power line that runs throught the back yard even though I have it guyed from 3 directions.
Would the hex beam be acceptable for receiving 360 degrees thereby eliminating the need for the vertical?