Having found more information since first posting my question, I think it beneficial for me to consolidate my findings and those contributed by my fellow answerers.
The original question sought to understand the impact of halving (or multiplying) a character's speed in an area affected by a spell, which in this case has a 15' radius of effect.
I will break my answer into two parts, the first comparing "Movement" and "Speed", the second addressing the particulars of my original question and using movement within a round.
Part 1: Movement and Speed
The word "speed" is used interchangeably with "movement" in the PHB. There is little doubt that "speed" and "movement" are two words for the same thing: the former connotes the ability to travel notable distances, whereas the latter connotes short-distance movement in combat.
The PHB addresses time and movement in its chapter Adventuring, and it there makes clear that combat is a subset of adventuring (which is intuitively obvious) when it states on page 181 under Time:
In combat and other fast-paced situations, the game relies on rounds, a 6-second span of time described in chapter 9.
Under its table Travel Pace, on page 182, the PHB divides the Fast, Normal, and Slow spaces into time distances of Minute, Hour, and Day, which are directly proportional to a standard character's single Round movement of 30 feet per six seconds. There is thus no difference between traveling ability and combat movement ability other than time scale.
During adventuring movement, there is a speed-altering category called difficult terrain which impacts travel and combat alike and has clearly defined effects. A character moving through difficult terrain is said to move at half speed. Under the heading Difficult Terrain on page 190, the PHB defines half speed as follows:
You move at half speed in difficult terrain—moving 1 foot in difficult terrain costs 2 feet of speed—so you can cover only half the normal distance in a minute, an hour, or a day.
Whether or not a spell's AoE counts as "difficult terrain", "half speed" is clearly defined as "moving 1 foot ... costs 2 feet of speed".
Within the Combat chapter of the PHB, on page 190, when talking about difficult terrain, it says:
Every foot of movement in difficult terrain costs 1 extra foot.
So we see that difficult terrain is defined exactly the same way inside and outside combat, written in two slightly different ways to make the point clear.
Regarding having different speeds available to you, and easily extrapolating movement in and out of difficult terrain and spell effects, we read:
If you have more than one speed ... you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can't use the new speed during the current move.
The mechanisms for difficult terrain and spell areas of effect (and all movement everywhere in the PHB) are clearly interconnected and, in fact, the same.
Part 2: The Particulars of a Round
For the spell Spirit Guardians, which has a 15' radius,
An affected creature’s speed is halved in the area.
By "speed is halved", as above, we clearly understand "moving 1 foot ... costs 2 feet of speed" and "Every foot of movement ... costs 1 extra foot."
A character moving at 30 feet per round of speed would move at the equivalent rate of 15 feet per round inside the area of effect because each foot of movement would cost 2 feet of speed. @Alexis Wilke insightfully stated:
When you are slowed down, you just count each hexagon or square as 10 feet instead of the usual 5.
Here are a few scenarios:
- Our character moves 15 feet before crossing the border of the affected area. Having 15 feet of movement remaining, the character can move 7.5 feet within the area, rounded down to 7.
Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater. (PHB, 7)
- Our character starts at the center of the AoE and must move 15 feet to escape, at the cost of 30 feet to his movement for that round. Upon reading the border, he has has 0 feet of movement remaining. His total physical movement this turn is 15 feet.
- Our character starts 5 feet off of the center of the AoE and must move 10 feet to escape, at the cost of 20 feet. Upon reaching the border, he has 10 feet remaining of his 30 feet per round movement and, using it, moves a total of 20 feet this turn.
- @Alexis-Wilke also said:
As a side note, when going in diagonal (squares), you are authorized to see each square as a simple "1.5" the distance (which is close to square root of 2). So if you have 30 ft to walk in normal terrain you can go 4 squares in diagonal. (i.e. one square diagonal is 1.5 x 5 ft = 7.5 ft) You could apply similar math to slowed down straight line, but then it becomes complicated because you do not end up in one specific spot. Fights are clear if you are in a specific spot. Not in between two. So I would not allow it. You have to forfeit that last half movement.
If our character moving from the center crosses along the diagonal, the 15-foot radius of the spell matches two square diagonals of 7.5 feet each, and so he would escape the AoE by landing on the third square diagonally with 0 remaining movement.
Furthermore, we must remember that a round is
a 6-second span of time described in chapter 9.
Movement is given by the maximum distance a character can physically travel in a given span of time, in combat 6 seconds. If a character were to move as suggested in other comments, moving 15 feet to escape the half-speed area and then regaining a speed of 30 feet to move an additional 15, then the character, who has a base speed of 30 ft/6 sec = 5 ft/sec and a halved speed of 15 ft/6 sec = 2.5 ft/sec would move 15 feet at 2.5 ft/sec for 6 seconds followed by 15 feet at 5 ft/sec for 3 seconds for a total of not only 30 feet but also 9 seconds--in a 6-second round.
This is impossible without a time-dilation device or an effective speed of 45 feet per 6-second round. Effectively you are arguing that a character is not only moving faster than humanly (choose your race) possible--even faster than at a fast traveling pace--but that he is doing so while magically slowed down!