What caliber are your current darts? I guess at this point I am assuming 9mm or .40 caliber range. For match target shooting you will want to have small cones to allow closer grouping without hitting your own darts too often Robin Hood.
Before considering weight. I would recommend you build a set of darts any weight and style you like today but all near identical. Your final match darts will need to be so identical you don't know the difference unless they are marked with ID labels. Then, film your shooting in profile and chronograph it. Then, select a style of puff that propels with repeatable velocity for 10 shots in 3 minutes repeated 6 times in a row with no more than 30 seconds between sets. (Twice the number of shots taken in a match) and with minimal lurching. Once settled on a style don't puff or release differently for a few thousand shots at least.
Now, about the weight. What do your current darts weigh? I am thinking they weigh very close to 1 gram or 16 grains. For indoor shooting heavier darts have far less advantage. You only need enough weight to reliably anchor in the target. Also, I think your wire diameter of 1,2mm may invoke a wide lined target rule. 1,15mm does not. If exceeding the 0.047" diameter rule I would consider shafts all the way up to 3mm. Whatever shaft diameter I would always center sharpen the tip at a similar angle to an arrow field tip not too sharp but absolutely no one sided angle cut tips. You do not want the tip sharp enough that it ever bends or touches the tube wall. The touch point should be close to the edge of the shaft.
Use a shaft material that seldom bends. Your choice of spring steel is a good one. Never straighten a shaft. Discard every dart that ever bends noticeably. Your shaft material should come to you as a perfect rod and never on a roll of wire.
The shaft should only extend into the cone 5mm or so and should be firmly held in the cone centerline. Never allow the cones to be misaligned. This requires some fill material at the connection point inside the tip of the cone. Perhaps glue that will not accept moisture after drying.
Develop a method to swab your tube effectively in a few seconds at most to mitigate moisture build up. Then use that as an every day part of your protocol.
For outdoor shooting you will want to chronograph your darts with various weights and graph where the velocity begins to drop off noticeably.
If your velocities are uniform for all tested dart weights then look for the dart length that gives you personally the best accuracy.
What is your tube like? For competition target shooting I think 48" is the only length to consider appropriate as the penalty for longer tubes exceeds the benefit and there is no benefit allowed to a shorter tube. I would recommend you start with a one piece heavy wall 9mm, 10mm or .40 caliber tube made of T-6 aluminum. Absolutely no multiple piece tubes. Install the very best mouthpiece available and quality hand grips.
Establish holsters or something to allow exactly 5 darts per set to be available to you. Have spare darts elsewhere and readily available in case of a bounce shot. If you count shots manually during the set you will count wrong eventually or will focus on the count when you should be focusing on your shooting.
CG compared to length matters not one bit if your darts are shorter than 4-6" or possibly even a foot. CG is compared to center of drag and you really only need worry about CG if your darts are hitting target other than perpendicular and sloping ever so slightly down.
After all is done you may experiment with cone angles. It seems your current angles are reasonable So I would recommend leaving those as is until all other matters are settled. I think you will want sharp cones but do not get carried away with that.
Disclaimer: I have zero experience in match BG competition. Yep, zero.
