Not quite sure if this is a full answer to the question, but will try anyway.
Iran has an interesting position in this war as they were kinda neutral yet pro-german at points...both the Soviets and British had identified the chance of a pro-german coup in Iran. Baku, an oil field in present day Azerbaijan, was actively sending fuels to Germany prior to the war. However in March 1940 the soviets launched a full scale invasion of northern Iran and took Baku and it's oil fields.
The British also invaded (potentially with the support of the US) and attacked Iran, seizing the oil fields of Bander-I Shahpur and Abadan, destroying Irans fleet and air power in the process (The Shah in Iran compared Germany/Russia invasion of Poland to what the Allies did to Iran, the invasion was rapid and the spoils were quickly divided). I assume these are the oil fields you talk about to the south of the Caspian.
Not sure on how accurate this source is here, but it will suggest that Russia and the Allies nearly went to war themselves over Iranian oil.
Perhaps fortunately, the allied plans for a grand anti-soviet/German strategy collapsed when Finland did. Those plans included using bombers to attack the USSR, which would have almost certainly have provoked a soviet attack on Turkey and Iraq, causing massive disruption to the British Empire and their probable defeat. Further, the pathetic success rate of unguided bombers in 1939 suggests that, even if Stalin did not order retaliation, they would only hit empty land.
Despite this collapse, the soviets continued to move forces into the Baku region in March 1940. These forces were formidable, five infantry divisions, one tank division, a cavalry division and two light tank divisions. This new army group had about 200’000 men and nearly a thousand tanks. The soviets used this force to intimidate Iran, which the Germans gleefully noted, and then tried to lure Iran into a German alliance. However, the Germans soon had other problems, as their attack on France soon caused her collapse and with her, much of the remaining allied strategy. Worse, soviet pressure on Iran intensified to a point in which Britain first considered breaking Iranian neutrality and occupying or destroying the oil refineries.
Stubbornly, the Shah refused to compromise with Russia, despite the Iranian military realising that a defence of the soviet target areas was impossible. However, Stalin reduced pressure in August, apparently out of the concern that the British might attack the soviet oil wells if he invaded.
As a simplistic answer:
Were there alternate sources of oil from Iran available to the Soviet Union
Not really due to British involvement. By the time Hitler attacked Russia, these oil fields were in British hands. I believe the same goes with Iraqi oil fields further south.
If Russia lost it's Baku oil, I believe Siberia might be the only remaining option.
A second source for verification. http://www.iranreview.org/content/Documents/World-War-II-Anglo-Soviet-Invasion-of-Iran.htm