There are two approaches you can take.
1) Combine cheaper items of Class 3 to T3 and transfer onto Gnome Helmet making it T2 Gnome Helmet. Then repeat the process to get another T2 Gnome Helmet and combine both.
A good candidate is Embrace Of Nature as it's generally the cheapest Class 3 item.
You would need:
8x embrace of nature
1x gnome helmet
Cash:
4x 4kk for combining items to T1
2x 10kk to T2
1x 20kk to T3
1x 20kk for transfer from T3 Embrace to T2 Gnome
= 76kk
This would result in T2 Gnome Helmet so now you would have to do it all over again to get another T2 Gnome Helmet - everything on the list above would be doubled. Now you need to combine two T2 Gnome Helmets for an additional 20kk.
Total cost for T3 Gnome Helmet: 16 embraces of natures, 2 gnome helmets, 172kk.
At the price of 300k for Embrace and 20kk for Gnome, this would be ~45kk so the total cost is 217kk.
2) Other way using only Gnome Helmets:
8 gnome helmets
Cash:
4x 4kk for four T1 helmets
2x 10kk for two T2 helmets
1x 20kk for T3 helmet
= 56kk
So 8 Gnome Helmets and 56kk.
At the price of 20kk for Gnome Helmet, it would be 216kk.
Those calculations do not include dust and slivers - the method with Embraces requires more forge attempts so it would consume more of those resources.
Potential fails are also not included and if you happen to fail (especially at later attempts) it can increase the cost by a lot.
I am playing on a fairly new server where the price of Gnome Helmet is around 20-25kk, it's probably cheaper on older words so you would need to adjust for the price.