When I first got my 7x57 I tried 140 bulk bullets and the 145gr Grand Slams. Couldn't tell you why, it was just what I found first. They would not shoot better than 1 1/2" for a hundred yards not matter what length they were seated, the charge behind them or the powder or case used. Quite frustrating.
Then I tried 154 gr Interbonds, using the H414 and CCI250's and RP brass.
Most times I am shooting 1" groups but they have gone as small as .400" with that bullet. I was seating this bullet as long as possible to get close to the lands and still the accuracy was not always repeatable.
For entertainment value I tried a box of standard 154gr Interlock round noses and seated them to the first edge of the cannelure with the cases trimmed 5 thou longer than the RCBS manuals trim length. It was purely by fluke I came across the load, when I did not double check the box of bullets I was handed at WSS. The results I came up with had me all smiles. Just about as good as the Interbonds but they maintain the same tight groups more repeatedly.
I tried the Interlock Spire points at the same length I was using the Interbonds with but had no sucess there at all. Instead I tried a different approach. I used my vernier caliper set at .280" and lightly rotated the round nose in the jaws so it would etch a small line around the circumference of the ogive. Then I did the same with the spire point of the same weight.
Next I seated the spire point in a case to the same point as the round nose so both etched lines in each projectile were at the same position. Basically putting them both the same distance from the lands of the barrel. Just like that the groups went from 1 3/4" to well inside an inch at 100 yds.
Some loads you fight tooth and nail for, others just fall in your lap.
First things first
-bedding of the rifle, is it cracked or shrunk so it isn't supporting the lugs?
-trigger, my Brno had a single set but it was grim at best. A Dayton really cleaned it up, you don't have to wonder how much it will creep before going off.
- damage to the crown or erroded throat could cause you trouble too.
Personally I think you are on the right track with the 414 powder. If the other bases here are proved, just try some different projectiles.
Hope this helps.