There seems to be a progressive deterioration in accuracy for the Handi rifles as the pressure specs of the cartridge for which it is chambered increase. Not talking about your rifle that shoots 1/2" all day but rather the Handi rifles in general. The higher the pressure, the more severe become the vibrations and general shakin rattllin and rollin of the frame to barrel lock-up.
I agree with Fred on the quality of factory ammo these days but also think that for the most part getting an accurate load for a Handi involves handloading. There are some factory loads that seem to shoot nearly universally well in the Handi. The 223 Win Varm Pak is a good example. OTOH, I've not seen any one factory load for the .270 get raves for near universal accuracy results in the Handi. There are always going to be reports of exceptional results with a given factory 270 load but I don't recall any getting an overwhelming thumbs up.
My suggestion, once all the loose screws and nuts are tightened, is to handload for the rifle. If you aren't a handloader, become one. You can do it for less than $150 bucks. You are going to spend way more than that on factory ammo trying to find an accurate load, and then the factory load bullet/velocity, etc. may not be ideal for your field application.
Get set up and select a good quality bullet that will provide the terminal performance that you want. Then pick a powder that is considered to be a good powder for that cartridge and that bullet weight (eg., 130 grain bullet matched to 4350, 4831, RL19 or RL22). Then select a primer appropriate for the powder/case. Next, start about 5% below the max recommended load and load five rounds. Then move up 3/10ths of a grain and load five more rounds (weigh each charge). Keep doing that until you have loaded five rounds for each increment of 3/10ths grain until your last five rounds are at max. For the 270, you are going to have 9 or 10 loads or 45 or 50 rounds.
When you shoot these, shoot a few foulers first and then shoot a group with each load starting at the lowest charge and work your way up through the loads. Let the barrel cool either between groups or between shots (whichever, be consistent) If you plan to clean the barrel during the test, clean after each group and fire a few foulers after each cleaning. You should do this during ideal weather condidtions. Mainly, no wind! If the wind starts up or you get tired and feeling flinchy, stop and continue another day. Take four or five range sessions if need be!
Fire each group at a different target. Save the targets. When finished, compare the groups. Look for a trend. Hopefully you will see a tendency for groups to tighten and possibley open with the tightest point being close to an ideal charge for that bullet and powder.
If there is no improvement in any of the above groups, then something is probably loose or the rifle may not be able to do any better. You can try the same procedure with other bullet weights and powder combos but, IMO, if the rifle does not show a trend toward better grouping with one or three of the charges tested, you may be wasting your time and money on a rifle that has already shown you it's best.
Others will disagree with the above, but I'll stand by it and recommend you try it.