Reducing tax obligation for LLC electing S-corp taxation

First off, let's correct or clarify some of your assumptions about S-Corp taxation. Note these are basic simplifications and do take into consideration the various tweaks due to tax laws or income brackets:

1. With Payroll, there are company and employee expenses. So, to hit your $30 amount, you would pay yourself $27.87, and then both you and the company would pay 7.65% FICA taxes, so the company would add on $2.13 in FICA (meaning the company pays $30 total), and then you would also pay $2.13 in FICA, and perhaps pay an additional $5.74 in state and federal taxes to get your take home down to $20. (Why this is spelled out will become clear down below.)
2. There is no federal company tax for an S-Corp. (Note some states do charge a small tax on S-Corps.)
3. In your example, the total company expenses are Payroll ($30) + Other operational expenses ($15). Total expenses are $45 and so company income (profit) is $55. With an S-Corp (and LLC taxed as an S-Corp), that $55 flows through to you.
4. Your personal tax liability is now $27.87 (your W2 wages) + $55 = $82.87. This is what you would pay your federal and state taxes based on. Suppose your state + fed tax rate is 25%, then your total tax liability is $20.72. Note that you have already paid $5.74 in taxes as part of your W2 wages withholding, so your total additional tax liability is $20.72-5.74 = $14.98.
5. Distributions do not have any tax liability. If you leave the money in the company, or take it out, it makes no difference from a tax stand point (unless you distribute more than you have and go into debt, then there is a tax penalty.) Typically, owners will choose to distribute at least the amount needed to cover the taxes, so in this case you might distribute $14.98 so you can pay the tax without having to personally come up with the money for it.
6. Note from a tax savings point of view, the difference between LLC as an S-Corp, vs a typical LLC or sole proprietorship, is basically just the FICA savings. Without the S-Corp you would also have to pay the addition combined 15.3% FICA tax on the $55, which would be $8.24 in additional FICA taxes. Note that would reduce the company profit by half of that amount ($4.12), which would also reduce your personal tax liability by that amount, meaning you would only owe fed and state taxes on $78.75 instead of $82.87. So you would pay $8.24 in extra FICA, but save $1.03 in income taxes, for a net savings of $7.21 by electing S-Corp.

As for additional ways to reduce your tax burden, it basically comes down to increasing your expenses. You can't create fake expenses that don't have a corresponding payment coming out of your bank account (or CC statement), but you oftentimes can shift some personal expenses into your business and count them as an expense. For example, if you use your cell phone for business, a portion of your cell phone bill could be expensed to the business. Similarly for a new laptop, monitor, or gas used (or miles but not both) when you drive to and from clients.

Note in general, you are always better off having less expenses instead of more, because even though less expenses translates to more profit and more tax, it also mean more money is leftover for you, which is typically the ultimate goal of a for-profit business.