At the end of the day, you should do whatever makes sense to you based on what you are trying to accomplish in your sheets.
However, you might consider the following:
I assume you have a taxable brokerage account. Link the brokerage account to Tiller. Code all transfers into and out of the brokerage account as transfers. Code all the activity occurring in the brokerage account as transfers, except for dividends (income), interest (income), and fees (expense). When you have a sale transaction, make a manual transaction and code any gain as (income) and any loss as (expense). The balance sheet side of things will take care of itself since the brokerage account is linked to Tiller.
Treating the transfers into and out of the brokerage account as income or expense has the potential to clutter up your P&L which you can and should generate from Tiller. Coding as transfers can be cleaner since you can hide those transfer categories. Either way, the net end result to the P&L should be the same.
Your online brokerage account tracks tax basis by lot. Given this is a taxable account, when you sell you can use the specific identification method versus FIFO, LIFO, etc. If you want to change the tax lot sold after you have made the sell trade, you have until the settlement date which is two business days after the trade date. This has saved me on more than one occasion.
Since it appears you might be using these transfers for short term needs, you might consider investing those funds into a safer investment vehicle, such as a savings account, online saving account, CD, etc. Investing in stocks exposes you to more risk than you might want to assume. Your goal should be safety in principal, not potential for income.
I hope this is helpful.
Cheers,
Blake