A quick calculation (your pay increase of $20k/yr times 40%, an estimate of your marginal tax rate inclusive of FICA) suggests your withholding should increase by $8000 per year, or a little over $300 every 2 weeks. Your thought of "increase withholding by 30% of the old withholding" would fall considerably short -- my rough estimate is that your withholding increases by 90% or so from the $344 you mentioned.
Either your old withholding was far too low, or else the "Two Earners Worksheet" makes an assumption that does not apply to your situation (for example, assuming you have been making the higher salary all year, but spreading the extra tax over only 7 pay periods instead of all 26).
My suggestion would be instead of filling out the $780 on the W4, to list zero extra withholding and set that much aside into a savings account every paycheck. That way you will be able to pay the tax due when you file your 2019 taxes (you will have tax due, but it will be less than the worksheet is calculating). As long as your withholdings are greater than 110% of last year's total tax, you won't owe any penalty. If you keep control over the money until filing time, you (a) can earn some interest on it over the next 7 months and (b) have the difference available to you immediately when you file, instead of waiting for the IRS to process a refund.
Next year you will fill out the W4 again, and this time the "Two Earners" calculation will be properly divided out over a whole year. (If you do it in January; don't wait until tax filing to update the W4)