Hi templehof1. In terms of your own UK Self Assessment tax return, it sounds about right that you (personally) won't be eligible for split-year treatment under the Statutory Residence Test in your circumstances, but if you did not earn any income after leaving the UK then you will not need to make any claim under the UK-Germany double tax agreement. Your tax return will just show you as resident for the whole year and you will need to report your worldwide income earned up to the point you left.
Your husband's position is clearly more complicated and you should consider getting professional support to file the UK return. If he is not eligible for split-year treatment (again, this seems plausible from the circumstances you describe) then your next step is to consider where he is resident for the purposes of Article 4 of the UK-Germany Double Tax Agreement and for what period (i.e. where he is 'treaty-resident'). The first step here is to work out from what point your husband is treated as resident in Germany under domestic German law, then for the periods where he is resident both in the UK (under domestic UK law) and in Germany (under domestic German law), you consider the tie-breaker tests in Article 4(2) of the treaty, which start by looking at where he has a 'permanent' home.
Assuming your husband is treaty-resident in Germany from August, strictly speaking you'll need to make a claim for the German income earned from August using helpsheet HS302 (https://www.gov.uk/government/publications/dual-residents-hs302-self-assessment-helpsheet) which you should attach to the UK return. The guidance notes to the HS302 are somewhat misleading as they say "You can claim full or partial relief on UK tax on your UK income if the 2 countries have a double tax agreement that allows you to do so", but the form is equally appropriate for non-UK income which would otherwise be taxable in the UK. You suggest your husband has income from both self-employment and employment - where the income is exempt from UK tax under the relevant article of the treaty you should set this out in the table on page 4 of the HS302 with a separate line for each source of income. This income should be excluded from the main return and the German taxes which were deducted on the income should be ignored. If the self-employment income is a loss (under UK rules), then you can just exclude this from the claim.
I hope that helps but if you need further support then feel free to PM me.