Return flight is 31 days after arrival, Egypt visa-on-arrival is 30 days, will I be allowed to board?

I have a return ticket from Germany (Frankfurt) to Egypt (Cairo). The return date is 31 days after the arrival date.
The tourist visa-on-arrival is 30 days for German citizens.
Presently my plan is not to apply for a 90 day tourist visa before hand.
I intend leaving Egypt via Sudan overland.
I do not know how long I will be in Egypt. My plan was to extend my visa in Egypt if this is necessary.
I am flying Egypt Air.
Questions
- Will I be allowed to board the aircraft without a visa?
- Or should I get a 90 day visa before departure?
- Or should I change the return date of my ticket which costs money :( ?.
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Can I stay longer than 30 days in Egypt?
There is also a multiple-entry visa option, permitting tourists to travel to Egypt multiple times over a 180-day period. The total number of days spent in Egypt cannot exceed 30 days per entry over this duration. If your Egypt visa has expired, renewing the Egypt e-Visa is just as simple as the original process.How does visa on Arrival work in Egypt?
Travellers who wish to pay for their visa by card need to apply online, all major credit and debit cards are accepted. With an Egyptian visa on arrival, visitors can stay in the country for up to 30 days. It is a single-entry permit.Is Egypt visa multiple-entry?
Visitors who wish to leave and re-enter Egypt cannot do so with a single-entry visa, it is necessary to have a multiple-entry visa. Multiple-entry visas for Egypt are valid for 180 days and allow travelers to spend a total of up to 30 days per entry in the country.Do you need a visa for a connecting flight in Egypt?
Travelers can spend a limited time in Egypt visa-free between flights. Foreigners do not need a transit visa to stay for up to 48 hours. Transit passengers at Cairo airport can take advantage of facilities including restaurants, shops, banks, and business facilities.How to get an Egypt tourist visa on arrival | $25USD
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