No, there's no TurboTax product that will fulfill this need.
You have a good idea in sending in your Form 8835 with Form 8453, but it just won't satisfy IRS rules. As JulieS notes above, you'll need to print and mail your return.
The instructions for Form 8453, U.S. Individual Income Tax Transmittal for an IRS e-file Return are very specific: Don’t attach any form or document that isn’t shown on Form 8453 next to the checkboxes. If you are required to mail in any documentation not listed on Form 8453, you can’t file the tax return electronically.
You can't just send in Form 8835 on its own, either -- it must be attached to a paper return, else you'll get a letter from the IRS requesting it, delaying the processing your return. IRS tax examiners are instructed to correspond for the form if it's missing.
