I realize this could be a concern on your end. But I do think that more eggs is a good thing. However I realize you may be concerned that the overall affect of changing this would be to increase the total amount of eggs on the server by 25% * 50% of the base value. So below you will find the calculation to do what I propose above without increasing the total eggs dropped per adventure server wide.
A couple of calculations are needed to make this happen. We need the current average payout per adventure and we need to compute what the new base number should be considering that the three tiers will now be paying 1/2 base, base, and 2x base.
This is fairly straight forward although it takes a lot of words to describe what the numbers are.
Current average payout... Base * .55 + Bonus * .2 = P
Then we need the new base payout value. This comes from the current average payout divided by a constant. This has to be done for each adventure. You are probably using a table with 3 entries for each adventure.
So the entry for Black Knight might look something like
BK 0, 45, 90.
The average payout for BK is currently 45*.55 + 90*.2 = 42.75
We need to spread this average into the same three tiers as before but with a non-zero value in the lowest tier. The equation for that is
.5x + x + 2x = 42.75
x = 12.2
We then need to scale (adjust if you prefer) this number to the current average payout equation.
(.25*.5*12.2) + (.55*12.2) + (.2*.2*12.2) = 13.115
13.115/12.2 = 1.075
This 1.075 is a constant that represents the ratio between the old payout method and the new one and so we can shortcut some of the above calculations for each adventure.
42.75 is the current average payout. The new base is determined by the current average payout divided by a constant 1.075. So 42.75 / 1.075 = new base = 39.77. We will call that 40.
The constant is determined from the current probability tiers and the desire to have the new payouts conform to the 1/2x base, base and 2x base values.
The equation for that is (.5x *.25) + .55x + (.2x * 2) X = 1.075
So the new base is 40. The BK table entry will look like
BK: 20, 40, 80
If we calculate the new average payout based on these number we get .25*.25 + .55*40 + .2*80 = 43 Compare to the original average payout number of 42.75.
Doing one more example using Witch of the Swamp numbers,
WotS 0, 30, 50 --- the average is 26.5
26.5 / 1.075 = 24.65 rounds to 25. So 25 is the new base.
WotS 13, 25, 50 --- the new average is 27
I think these numbers are close enough that it will not cause any server egg inflation and players get eggs everytime they run an adventure.